analysis.inner_product_space.symmetric

Changes since the initial port

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.

Changes in mathlib3

3f655f52

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

0b7c740e

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -37,11 +37,11 @@ self-adjoint, symmetric
 -/
 
 
-open IsROrC
+open RCLike
 
 open scoped ComplexConjugate
 
-variable {𝕜 E E' F G : Type _} [IsROrC 𝕜]
+variable {𝕜 E E' F G : Type _} [RCLike 𝕜]
 
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
@@ -158,9 +158,9 @@ theorem IsSymmetric.restrict_invariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric
 
 #print LinearMap.IsSymmetric.restrictScalars /-
 theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
-    @LinearMap.IsSymmetric ℝ E _ _ (InnerProductSpace.isROrCToReal 𝕜 E)
-      (@LinearMap.restrictScalars ℝ 𝕜 _ _ _ _ _ _ (InnerProductSpace.isROrCToReal 𝕜 E).toModule
-        (InnerProductSpace.isROrCToReal 𝕜 E).toModule _ _ _ T) :=
+    @LinearMap.IsSymmetric ℝ E _ _ (InnerProductSpace.rclikeToReal 𝕜 E)
+      (@LinearMap.restrictScalars ℝ 𝕜 _ _ _ _ _ _ (InnerProductSpace.rclikeToReal 𝕜 E).toModule
+        (InnerProductSpace.rclikeToReal 𝕜 E).toModule _ _ _ T) :=
   fun x y => by simp [hT x y, real_inner_eq_re_inner, LinearMap.coe_restrictScalars]
 #align linear_map.is_symmetric.restrict_scalars LinearMap.IsSymmetric.restrictScalars
 -/
@@ -213,7 +213,7 @@ theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymm
       simp_rw [h, MulZeroClass.mul_zero, add_zero]
       norm_cast
   · simp_rw [map_add, map_sub, inner_add_left, inner_add_right, inner_sub_left, inner_sub_right,
-      LinearMap.map_smul, inner_smul_left, inner_smul_right, IsROrC.conj_I, mul_add, mul_sub,
+      LinearMap.map_smul, inner_smul_left, inner_smul_right, RCLike.conj_I, mul_add, mul_sub,
       sub_sub, ← mul_assoc, mul_neg, h, neg_neg, one_mul, neg_one_mul]
     ring
 #align linear_map.is_symmetric.inner_map_polarization LinearMap.IsSymmetric.inner_map_polarization

0b7c740e

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
 -/
-import Mathbin.Analysis.InnerProductSpace.Basic
-import Mathbin.Analysis.NormedSpace.Banach
-import Mathbin.LinearAlgebra.SesquilinearForm
+import Analysis.InnerProductSpace.Basic
+import Analysis.NormedSpace.Banach
+import LinearAlgebra.SesquilinearForm
 
 #align_import analysis.inner_product_space.symmetric from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"

0b7c740e

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.symmetric
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.InnerProductSpace.Basic
 import Mathbin.Analysis.NormedSpace.Banach
 import Mathbin.LinearAlgebra.SesquilinearForm
 
+#align_import analysis.inner_product_space.symmetric from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # Symmetric linear maps in an inner product space

0b7c740e

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -54,7 +54,6 @@ variable [NormedAddCommGroup G] [InnerProductSpace 𝕜 G]
 
 variable [NormedAddCommGroup E'] [InnerProductSpace ℝ E']
 
--- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
 
 namespace LinearMap
@@ -74,39 +73,52 @@ section Real
 
 variable ()
 
+#print LinearMap.isSymmetric_iff_sesqForm /-
 /-- An operator `T` on an inner product space is symmetric if and only if it is
 `linear_map.is_self_adjoint` with respect to the sesquilinear form given by the inner product. -/
 theorem isSymmetric_iff_sesqForm (T : E →ₗ[𝕜] E) :
     T.IsSymmetric ↔ @LinearMap.IsSelfAdjoint 𝕜 E _ _ _ (starRingEnd 𝕜) sesqFormOfInner T :=
   ⟨fun h x y => (h y x).symm, fun h x y => (h y x).symm⟩
 #align linear_map.is_symmetric_iff_sesq_form LinearMap.isSymmetric_iff_sesqForm
+-/
 
 end Real
 
+#print LinearMap.IsSymmetric.conj_inner_sym /-
 theorem IsSymmetric.conj_inner_sym {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) (x y : E) :
     conj ⟪T x, y⟫ = ⟪T y, x⟫ := by rw [hT x y, inner_conj_symm]
 #align linear_map.is_symmetric.conj_inner_sym LinearMap.IsSymmetric.conj_inner_sym
+-/
 
+#print LinearMap.IsSymmetric.apply_clm /-
 @[simp]
 theorem IsSymmetric.apply_clm {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →ₗ[𝕜] E)) (x y : E) :
     ⟪T x, y⟫ = ⟪x, T y⟫ :=
   hT x y
 #align linear_map.is_symmetric.apply_clm LinearMap.IsSymmetric.apply_clm
+-/
 
+#print LinearMap.isSymmetric_zero /-
 theorem isSymmetric_zero : (0 : E →ₗ[𝕜] E).IsSymmetric := fun x y =>
   (inner_zero_right x : ⟪x, 0⟫ = 0).symm ▸ (inner_zero_left y : ⟪0, y⟫ = 0)
 #align linear_map.is_symmetric_zero LinearMap.isSymmetric_zero
+-/
 
+#print LinearMap.isSymmetric_id /-
 theorem isSymmetric_id : (LinearMap.id : E →ₗ[𝕜] E).IsSymmetric := fun x y => rfl
 #align linear_map.is_symmetric_id LinearMap.isSymmetric_id
+-/
 
+#print LinearMap.IsSymmetric.add /-
 theorem IsSymmetric.add {T S : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (hS : S.IsSymmetric) :
     (T + S).IsSymmetric := by
   intro x y
   rw [LinearMap.add_apply, inner_add_left, hT x y, hS x y, ← inner_add_right]
   rfl
 #align linear_map.is_symmetric.add LinearMap.IsSymmetric.add
+-/
 
+#print LinearMap.IsSymmetric.continuous /-
 /-- The **Hellinger--Toeplitz theorem**: if a symmetric operator is defined on a complete space,
   then it is automatically continuous. -/
 theorem IsSymmetric.continuous [CompleteSpace E] {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) :
@@ -124,7 +136,9 @@ theorem IsSymmetric.continuous [CompleteSpace E] {T : E →ₗ[𝕜] E} (hT : Is
   rw [← sub_self x]
   exact hu.sub_const _
 #align linear_map.is_symmetric.continuous LinearMap.IsSymmetric.continuous
+-/
 
+#print LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply /-
 /-- For a symmetric operator `T`, the function `λ x, ⟪T x, x⟫` is real-valued. -/
 @[simp]
 theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →ₗ[𝕜] E))
@@ -135,24 +149,30 @@ theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymm
   rw [← conj_eq_iff_real]
   exact hT.conj_inner_sym x x
 #align linear_map.is_symmetric.coe_re_apply_inner_self_apply LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply
+-/
 
+#print LinearMap.IsSymmetric.restrict_invariant /-
 /-- If a symmetric operator preserves a submodule, its restriction to that submodule is
 symmetric. -/
 theorem IsSymmetric.restrict_invariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) {V : Submodule 𝕜 E}
     (hV : ∀ v ∈ V, T v ∈ V) : IsSymmetric (T.restrict hV) := fun v w => hT v w
 #align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariant
+-/
 
+#print LinearMap.IsSymmetric.restrictScalars /-
 theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
     @LinearMap.IsSymmetric ℝ E _ _ (InnerProductSpace.isROrCToReal 𝕜 E)
       (@LinearMap.restrictScalars ℝ 𝕜 _ _ _ _ _ _ (InnerProductSpace.isROrCToReal 𝕜 E).toModule
         (InnerProductSpace.isROrCToReal 𝕜 E).toModule _ _ _ T) :=
   fun x y => by simp [hT x y, real_inner_eq_re_inner, LinearMap.coe_restrictScalars]
 #align linear_map.is_symmetric.restrict_scalars LinearMap.IsSymmetric.restrictScalars
+-/
 
 section Complex
 
 variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℂ V]
 
+#print LinearMap.isSymmetric_iff_inner_map_self_real /-
 /-- A linear operator on a complex inner product space is symmetric precisely when
 `⟪T v, v⟫_ℂ` is real for all v.-/
 theorem isSymmetric_iff_inner_map_self_real (T : V →ₗ[ℂ] V) :
@@ -172,9 +192,11 @@ theorem isSymmetric_iff_inner_map_self_real (T : V →ₗ[ℂ] V) :
     norm_num
     ring
 #align linear_map.is_symmetric_iff_inner_map_self_real LinearMap.isSymmetric_iff_inner_map_self_real
+-/
 
 end Complex
 
+#print LinearMap.IsSymmetric.inner_map_polarization /-
 /-- Polarization identity for symmetric linear maps.
 See `inner_map_polarization` for the complex version without the symmetric assumption. -/
 theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (x y : E) :
@@ -198,7 +220,9 @@ theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymm
       sub_sub, ← mul_assoc, mul_neg, h, neg_neg, one_mul, neg_one_mul]
     ring
 #align linear_map.is_symmetric.inner_map_polarization LinearMap.IsSymmetric.inner_map_polarization
+-/
 
+#print LinearMap.IsSymmetric.inner_map_self_eq_zero /-
 /-- A symmetric linear map `T` is zero if and only if `⟪T x, x⟫_ℝ = 0` for all `x`.
 See `inner_map_self_eq_zero` for the complex version without the symmetric assumption. -/
 theorem IsSymmetric.inner_map_self_eq_zero {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
@@ -210,6 +234,7 @@ theorem IsSymmetric.inner_map_self_eq_zero {T : E →ₗ[𝕜] E} (hT : T.IsSymm
   simp_rw [h _]
   ring
 #align linear_map.is_symmetric.inner_map_self_eq_zero LinearMap.IsSymmetric.inner_map_self_eq_zero
+-/
 
 end LinearMap

0b7c740e

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -42,7 +42,7 @@ self-adjoint, symmetric
 
 open IsROrC
 
-open ComplexConjugate
+open scoped ComplexConjugate
 
 variable {𝕜 E E' F G : Type _} [IsROrC 𝕜]

0b7c740e

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -74,12 +74,6 @@ section Real
 
 variable ()
 
-/- warning: linear_map.is_symmetric_iff_sesq_form -> LinearMap.isSymmetric_iff_sesqForm is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] (T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))), Iff (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T) (LinearMap.IsSelfAdjoint.{u1, u2} 𝕜 E (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (starRingEnd.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u1} 𝕜 _inst_1)) (sesqFormOfInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) T)
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] (T : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))), Iff (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) (LinearMap.IsSelfAdjoint.{u2, u1} 𝕜 E (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (sesqFormOfInner.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3) T)
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric_iff_sesq_form LinearMap.isSymmetric_iff_sesqFormₓ'. -/
 /-- An operator `T` on an inner product space is symmetric if and only if it is
 `linear_map.is_self_adjoint` with respect to the sesquilinear form given by the inner product. -/
 theorem isSymmetric_iff_sesqForm (T : E →ₗ[𝕜] E) :
@@ -89,41 +83,23 @@ theorem isSymmetric_iff_sesqForm (T : E →ₗ[𝕜] E) :
 
 end Real
 
-/- warning: linear_map.is_symmetric.conj_inner_sym -> LinearMap.IsSymmetric.conj_inner_sym is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.conj_inner_sym LinearMap.IsSymmetric.conj_inner_symₓ'. -/
 theorem IsSymmetric.conj_inner_sym {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) (x y : E) :
     conj ⟪T x, y⟫ = ⟪T y, x⟫ := by rw [hT x y, inner_conj_symm]
 #align linear_map.is_symmetric.conj_inner_sym LinearMap.IsSymmetric.conj_inner_sym
 
-/- warning: linear_map.is_symmetric.apply_clm -> LinearMap.IsSymmetric.apply_clm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.apply_clm LinearMap.IsSymmetric.apply_clmₓ'. -/
 @[simp]
 theorem IsSymmetric.apply_clm {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →ₗ[𝕜] E)) (x y : E) :
     ⟪T x, y⟫ = ⟪x, T y⟫ :=
   hT x y
 #align linear_map.is_symmetric.apply_clm LinearMap.IsSymmetric.apply_clm
 
-/- warning: linear_map.is_symmetric_zero -> LinearMap.isSymmetric_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric_zero LinearMap.isSymmetric_zeroₓ'. -/
 theorem isSymmetric_zero : (0 : E →ₗ[𝕜] E).IsSymmetric := fun x y =>
   (inner_zero_right x : ⟪x, 0⟫ = 0).symm ▸ (inner_zero_left y : ⟪0, y⟫ = 0)
 #align linear_map.is_symmetric_zero LinearMap.isSymmetric_zero
 
-/- warning: linear_map.is_symmetric_id -> LinearMap.isSymmetric_id is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2], LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 (LinearMap.id.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2], LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 (LinearMap.id.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric_id LinearMap.isSymmetric_idₓ'. -/
 theorem isSymmetric_id : (LinearMap.id : E →ₗ[𝕜] E).IsSymmetric := fun x y => rfl
 #align linear_map.is_symmetric_id LinearMap.isSymmetric_id
 
-/- warning: linear_map.is_symmetric.add -> LinearMap.IsSymmetric.add is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.add LinearMap.IsSymmetric.addₓ'. -/
 theorem IsSymmetric.add {T S : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (hS : S.IsSymmetric) :
     (T + S).IsSymmetric := by
   intro x y
@@ -131,9 +107,6 @@ theorem IsSymmetric.add {T S : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (hS : S.Is
   rfl
 #align linear_map.is_symmetric.add LinearMap.IsSymmetric.add
 
-/- warning: linear_map.is_symmetric.continuous -> LinearMap.IsSymmetric.continuous is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.continuous LinearMap.IsSymmetric.continuousₓ'. -/
 /-- The **Hellinger--Toeplitz theorem**: if a symmetric operator is defined on a complete space,
   then it is automatically continuous. -/
 theorem IsSymmetric.continuous [CompleteSpace E] {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) :
@@ -152,9 +125,6 @@ theorem IsSymmetric.continuous [CompleteSpace E] {T : E →ₗ[𝕜] E} (hT : Is
   exact hu.sub_const _
 #align linear_map.is_symmetric.continuous LinearMap.IsSymmetric.continuous
 
-/- warning: linear_map.is_symmetric.coe_re_apply_inner_self_apply -> LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.coe_re_apply_inner_self_apply LinearMap.IsSymmetric.coe_reApplyInnerSelf_applyₓ'. -/
 /-- For a symmetric operator `T`, the function `λ x, ⟪T x, x⟫` is real-valued. -/
 @[simp]
 theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →ₗ[𝕜] E))
@@ -166,18 +136,12 @@ theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymm
   exact hT.conj_inner_sym x x
 #align linear_map.is_symmetric.coe_re_apply_inner_self_apply LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply
 
-/- warning: linear_map.is_symmetric.restrict_invariant -> LinearMap.IsSymmetric.restrict_invariant is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariantₓ'. -/
 /-- If a symmetric operator preserves a submodule, its restriction to that submodule is
 symmetric. -/
 theorem IsSymmetric.restrict_invariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) {V : Submodule 𝕜 E}
     (hV : ∀ v ∈ V, T v ∈ V) : IsSymmetric (T.restrict hV) := fun v w => hT v w
 #align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariant
 
-/- warning: linear_map.is_symmetric.restrict_scalars -> LinearMap.IsSymmetric.restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.restrict_scalars LinearMap.IsSymmetric.restrictScalarsₓ'. -/
 theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
     @LinearMap.IsSymmetric ℝ E _ _ (InnerProductSpace.isROrCToReal 𝕜 E)
       (@LinearMap.restrictScalars ℝ 𝕜 _ _ _ _ _ _ (InnerProductSpace.isROrCToReal 𝕜 E).toModule
@@ -189,9 +153,6 @@ section Complex
 
 variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℂ V]
 
-/- warning: linear_map.is_symmetric_iff_inner_map_self_real -> LinearMap.isSymmetric_iff_inner_map_self_real is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric_iff_inner_map_self_real LinearMap.isSymmetric_iff_inner_map_self_realₓ'. -/
 /-- A linear operator on a complex inner product space is symmetric precisely when
 `⟪T v, v⟫_ℂ` is real for all v.-/
 theorem isSymmetric_iff_inner_map_self_real (T : V →ₗ[ℂ] V) :
@@ -214,9 +175,6 @@ theorem isSymmetric_iff_inner_map_self_real (T : V →ₗ[ℂ] V) :
 
 end Complex
 
-/- warning: linear_map.is_symmetric.inner_map_polarization -> LinearMap.IsSymmetric.inner_map_polarization is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.inner_map_polarization LinearMap.IsSymmetric.inner_map_polarizationₓ'. -/
 /-- Polarization identity for symmetric linear maps.
 See `inner_map_polarization` for the complex version without the symmetric assumption. -/
 theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (x y : E) :
@@ -241,9 +199,6 @@ theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymm
     ring
 #align linear_map.is_symmetric.inner_map_polarization LinearMap.IsSymmetric.inner_map_polarization
 
-/- warning: linear_map.is_symmetric.inner_map_self_eq_zero -> LinearMap.IsSymmetric.inner_map_self_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.inner_map_self_eq_zero LinearMap.IsSymmetric.inner_map_self_eq_zeroₓ'. -/
 /-- A symmetric linear map `T` is zero if and only if `⟪T x, x⟫_ℝ = 0` for all `x`.
 See `inner_map_self_eq_zero` for the complex version without the symmetric assumption. -/
 theorem IsSymmetric.inner_map_self_eq_zero {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :

0b7c740e

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -142,9 +142,7 @@ theorem IsSymmetric.continuous [CompleteSpace E] {T : E →ₗ[𝕜] E} (hT : Is
   -- We prove it by using the closed graph theorem
   refine' T.continuous_of_seq_closed_graph fun u x y hu hTu => _
   rw [← sub_eq_zero, ← @inner_self_eq_zero 𝕜]
-  have hlhs : ∀ k : ℕ, ⟪T (u k) - T x, y - T x⟫ = ⟪u k - x, T (y - T x)⟫ :=
-    by
-    intro k
+  have hlhs : ∀ k : ℕ, ⟪T (u k) - T x, y - T x⟫ = ⟪u k - x, T (y - T x)⟫ := by intro k;
     rw [← T.map_sub, hT]
   refine' tendsto_nhds_unique ((hTu.sub_const _).inner tendsto_const_nhds) _
   simp_rw [hlhs]

0b7c740e

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.symmetric
-! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.LinearAlgebra.SesquilinearForm
 /-!
 # Symmetric linear maps in an inner product space
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines and proves basic theorems about symmetric **not necessarily bounded** operators
 on an inner product space, i.e linear maps `T : E → E` such that `∀ x y, ⟪T x, y⟫ = ⟪x, T y⟫`.
 
@@ -87,20 +90,14 @@ theorem isSymmetric_iff_sesqForm (T : E →ₗ[𝕜] E) :
 end Real
 
 /- warning: linear_map.is_symmetric.conj_inner_sym -> LinearMap.IsSymmetric.conj_inner_sym is a dubious translation:
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(IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T x) y)) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E 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-but is expected to have type
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(CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T x) y)) (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) y) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) y) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T y) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.conj_inner_sym LinearMap.IsSymmetric.conj_inner_symₓ'. -/
 theorem IsSymmetric.conj_inner_sym {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) (x y : E) :
     conj ⟪T x, y⟫ = ⟪T y, x⟫ := by rw [hT x y, inner_conj_symm]
 #align linear_map.is_symmetric.conj_inner_sym LinearMap.IsSymmetric.conj_inner_sym
 
 /- warning: linear_map.is_symmetric.apply_clm -> LinearMap.IsSymmetric.apply_clm is a dubious translation:
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_inst_3))}, (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (ContinuousLinearMap.LinearMap.coe.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) T)) -> (forall (x : E) (y : E), Eq.{succ u1} 𝕜 (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 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(IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 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_inst_3))) T x) y) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) x (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) T y)))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 (ContinuousLinearMap.toLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) T)) -> (forall (x : E) (y : E), Eq.{succ u2} 𝕜 (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) x) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) x) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))) T x) y) (Inner.inner.{u2, u1} 𝕜 E (InnerProductSpace.toInner.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3) x (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))) T y)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.apply_clm LinearMap.IsSymmetric.apply_clmₓ'. -/
 @[simp]
 theorem IsSymmetric.apply_clm {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →ₗ[𝕜] E)) (x y : E) :
@@ -109,10 +106,7 @@ theorem IsSymmetric.apply_clm {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →
 #align linear_map.is_symmetric.apply_clm LinearMap.IsSymmetric.apply_clm
 
 /- warning: linear_map.is_symmetric_zero -> LinearMap.isSymmetric_zero is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) 0 (OfNat.mk.{u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) 0 (Zero.zero.{u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.hasZero.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2], LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 (OfNat.ofNat.{u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) 0 (Zero.toOfNat0.{u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.instZeroLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric_zero LinearMap.isSymmetric_zeroₓ'. -/
 theorem isSymmetric_zero : (0 : E →ₗ[𝕜] E).IsSymmetric := fun x y =>
   (inner_zero_right x : ⟪x, 0⟫ = 0).symm ▸ (inner_zero_left y : ⟪0, y⟫ = 0)
@@ -128,10 +122,7 @@ theorem isSymmetric_id : (LinearMap.id : E →ₗ[𝕜] E).IsSymmetric := fun x
 #align linear_map.is_symmetric_id LinearMap.isSymmetric_id
 
 /- warning: linear_map.is_symmetric.add -> LinearMap.IsSymmetric.add is a dubious translation:
-lean 3 declaration is
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(AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))} {S : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) 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(Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (instHAdd.{u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.hasAdd.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) T S))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))} {S : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 S) -> (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 (HAdd.hAdd.{u1, u1, u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (instHAdd.{u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.instAddLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) T S))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.add LinearMap.IsSymmetric.addₓ'. -/
 theorem IsSymmetric.add {T S : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (hS : S.IsSymmetric) :
     (T + S).IsSymmetric := by
@@ -141,10 +132,7 @@ theorem IsSymmetric.add {T S : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (hS : S.Is
 #align linear_map.is_symmetric.add LinearMap.IsSymmetric.add
 
 /- warning: linear_map.is_symmetric.continuous -> LinearMap.IsSymmetric.continuous is a dubious translation:
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𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.continuous LinearMap.IsSymmetric.continuousₓ'. -/
 /-- The **Hellinger--Toeplitz theorem**: if a symmetric operator is defined on a complete space,
   then it is automatically continuous. -/
@@ -167,10 +155,7 @@ theorem IsSymmetric.continuous [CompleteSpace E] {T : E →ₗ[𝕜] E} (hT : Is
 #align linear_map.is_symmetric.continuous LinearMap.IsSymmetric.continuous
 
 /- warning: linear_map.is_symmetric.coe_re_apply_inner_self_apply -> LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 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(IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 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(DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 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_inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 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_inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) T)) -> (forall (x : E), Eq.{succ u1} 𝕜 ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real 𝕜 (HasLiftT.mk.{1, succ u1} Real 𝕜 (CoeTCₓ.coe.{1, succ u1} Real 𝕜 (IsROrC.algebraMapCoe.{u1} 𝕜 _inst_1))) (ContinuousLinearMap.reApplyInnerSelf.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T x)) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 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(NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) T x) x))
-but is expected to have type
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(PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 (ContinuousLinearMap.toLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) T)) -> (forall (x : E), Eq.{succ u2} 𝕜 (IsROrC.ofReal.{u2} 𝕜 _inst_1 (ContinuousLinearMap.reApplyInnerSelf.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T x)) (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) x) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) x) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))) T x) x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.coe_re_apply_inner_self_apply LinearMap.IsSymmetric.coe_reApplyInnerSelf_applyₓ'. -/
 /-- For a symmetric operator `T`, the function `λ x, ⟪T x, x⟫` is real-valued. -/
 @[simp]
@@ -184,10 +169,7 @@ theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymm
 #align linear_map.is_symmetric.coe_re_apply_inner_self_apply LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply
 
 /- warning: linear_map.is_symmetric.restrict_invariant -> LinearMap.IsSymmetric.restrict_invariant is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (forall {V : Submodule.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))} (hV : forall (v : E), (Membership.Mem.{u2, u2} E (Submodule.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) E (Submodule.setLike.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))) v V) -> (Membership.Mem.{u2, u2} E (Submodule.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) E (Submodule.setLike.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T v) V)), LinearMap.IsSymmetric.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) E (Submodule.setLike.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))) V) _inst_1 (Submodule.normedAddCommGroup.{u1, u2} 𝕜 E (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) V) (Submodule.innerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 V) (LinearMap.restrict.{u1, u2, u2} 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) T V V hV))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (forall {V : Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))} (hV : forall (v : E), (Membership.mem.{u1, u1} E (Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (Submodule.setLike.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) v V) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) v) (Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (Submodule.setLike.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T v) V)), LinearMap.IsSymmetric.{u2, u1} 𝕜 (Subtype.{succ u1} E (fun (x : E) => Membership.mem.{u1, u1} E (Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (Submodule.setLike.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) x V)) _inst_1 (Submodule.normedAddCommGroup.{u2, u1} 𝕜 E (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) _inst_2 (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) V) (Submodule.innerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 V) (LinearMap.restrict.{u2, u1, u1} 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) T V V hV))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariantₓ'. -/
 /-- If a symmetric operator preserves a submodule, its restriction to that submodule is
 symmetric. -/
@@ -196,10 +178,7 @@ theorem IsSymmetric.restrict_invariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric
 #align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariant
 
 /- warning: linear_map.is_symmetric.restrict_scalars -> LinearMap.IsSymmetric.restrictScalars is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (LinearMap.IsSymmetric.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (LinearMap.restrictScalars.{0, u1, u2, u2} Real 𝕜 E E Real.semiring (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{0, u2} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (NormedSpace.toModule.{0, u2} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (LinearMap.IsScalarTower.compatibleSMul.{u2, u2, 0, u1} E E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) Real 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (SMulZeroClass.toHasSmul.{0, u1} Real 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real 𝕜 (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real 𝕜 (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real 𝕜 (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) (Algebra.toModule.{0, u1} Real 𝕜 Real.commSemiring (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real 𝕜 Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1))))))) (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{0, u2} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (Real.isScalarTower.{u2, u1} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (NormedSpace.toModule.{0, u2} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (BoundedSMul.continuousSMul.{0, u2} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))))) (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{0, u2} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.boundedSMul.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))) (T25Space.t2Space.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (T3Space.t25Space.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (separated_t3.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (MetricSpace.to_separated.{u2} E (NormedAddCommGroup.toMetricSpace.{u2} E _inst_2))))) 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (NormedAlgebra.toAlgebra.{0, u1} Real 𝕜 Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (BoundedSMul.continuousSMul.{0, u1} Real 𝕜 Real.pseudoMetricSpace (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (SubNegMonoid.toAddMonoid.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (SeminormedAddGroup.toAddGroup.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))))) (SMulZeroClass.toHasSmul.{0, u1} Real 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real 𝕜 (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real 𝕜 (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real 𝕜 (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) (Algebra.toModule.{0, u1} Real 𝕜 Real.commSemiring (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real 𝕜 Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1))))))) (NormedSpace.boundedSMul.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1)))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))) (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{0, u2} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (Real.isScalarTower.{u2, u1} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (NormedSpace.toModule.{0, u2} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (BoundedSMul.continuousSMul.{0, u2} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))))) (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{0, u2} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.boundedSMul.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))) (T25Space.t2Space.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (T3Space.t25Space.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (separated_t3.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (MetricSpace.to_separated.{u2} E (NormedAddCommGroup.toMetricSpace.{u2} E _inst_2))))) 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (NormedAlgebra.toAlgebra.{0, u1} Real 𝕜 Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (BoundedSMul.continuousSMul.{0, u1} Real 𝕜 Real.pseudoMetricSpace (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (SubNegMonoid.toAddMonoid.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (SeminormedAddGroup.toAddGroup.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))))) (SMulZeroClass.toHasSmul.{0, u1} Real 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real 𝕜 (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real 𝕜 (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real 𝕜 (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) (Algebra.toModule.{0, u1} Real 𝕜 Real.commSemiring (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real 𝕜 Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1))))))) (NormedSpace.boundedSMul.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1)))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))) T))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (LinearMap.IsSymmetric.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3) (LinearMap.restrictScalars.{0, u2, u1, u1} Real 𝕜 E E (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (LinearMap.IsScalarTower.compatibleSMul.{u1, u1, 0, u2} E E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) Real 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (Algebra.toSMul.{0, u2} Real 𝕜 Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u2} Real 𝕜 Real.normedField (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{0, u1} Real E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (Real.isScalarTower.{u1, u2} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) (T25Space.t2Space.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (T3Space.t25Space.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (separated_t3.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (MetricSpace.to_separated.{u1} E (NormedAddCommGroup.toMetricSpace.{u1} E _inst_2))))) 𝕜 (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (NormedAlgebra.toAlgebra.{0, u2} Real 𝕜 Real.normedField (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (BoundedSMul.continuousSMul.{0, u2} Real 𝕜 Real.pseudoMetricSpace (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) Real.instZeroReal (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Algebra.toSMul.{0, u2} Real 𝕜 Real.instCommSemiringReal (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u2} Real 𝕜 Real.normedField (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1))) (NormedSpace.boundedSMul.{0, u2} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u2} Real Real.normedField 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1)))) (BoundedSMul.continuousSMul.{u2, u1} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (NormedSpace.boundedSMul.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{0, u1} Real E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (Real.isScalarTower.{u1, u2} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) (T25Space.t2Space.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (T3Space.t25Space.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (separated_t3.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (MetricSpace.to_separated.{u1} E (NormedAddCommGroup.toMetricSpace.{u1} E _inst_2))))) 𝕜 (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (NormedAlgebra.toAlgebra.{0, u2} Real 𝕜 Real.normedField (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (BoundedSMul.continuousSMul.{0, u2} Real 𝕜 Real.pseudoMetricSpace (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) Real.instZeroReal (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Algebra.toSMul.{0, u2} Real 𝕜 Real.instCommSemiringReal (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u2} Real 𝕜 Real.normedField (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1))) (NormedSpace.boundedSMul.{0, u2} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u2} Real Real.normedField 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1)))) (BoundedSMul.continuousSMul.{u2, u1} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (NormedSpace.boundedSMul.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))) T))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.restrict_scalars LinearMap.IsSymmetric.restrictScalarsₓ'. -/
 theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
     @LinearMap.IsSymmetric ℝ E _ _ (InnerProductSpace.isROrCToReal 𝕜 E)
@@ -213,10 +192,7 @@ section Complex
 variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℂ V]
 
 /- warning: linear_map.is_symmetric_iff_inner_map_self_real -> LinearMap.isSymmetric_iff_inner_map_self_real is a dubious translation:
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-  forall {V : Type.{u1}} [_inst_10 : NormedAddCommGroup.{u1} V] [_inst_11 : InnerProductSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10] (T : LinearMap.{0, 0, u1, u1} Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) V V (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11))), Iff 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(InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11))) V (fun (a : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V) a) (LinearMap.instFunLikeLinearMap.{0, 0, u1, u1} Complex Complex V V Complex.instSemiringComplex Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) T v) v)) (FunLike.coe.{1, 1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex (fun (_x : Complex) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Complex) => Complex) _x) (MulHomClass.toFunLike.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalNonAssocSemiring.toMul.{0} Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))) (NonUnitalRingHomClass.toMulHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) (RingHomClass.toNonUnitalRingHomClass.{0, 0, 0} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex))) Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (RingHom.instRingHomClassRingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.instCommSemiringComplex)))))) (starRingEnd.{0} Complex Complex.instCommSemiringComplex Complex.instStarRingComplexToNonUnitalSemiringToNonUnitalCommSemiringToNonUnitalCommRingCommRing) (Inner.inner.{0, u1} Complex ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V) v) (InnerProductSpace.toInner.{0, u1} Complex ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V) v) Complex.instIsROrCComplex _inst_10 _inst_11) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{0, 0, u1, u1} Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) V V (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11))) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, u1} Complex Complex V V Complex.instSemiringComplex Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) T v) v)) (Inner.inner.{0, u1} Complex ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V) v) (InnerProductSpace.toInner.{0, u1} Complex ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V) v) Complex.instIsROrCComplex _inst_10 _inst_11) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{0, 0, u1, u1} Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) V V (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11))) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, u1} Complex Complex V V Complex.instSemiringComplex Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) T v) v))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric_iff_inner_map_self_real LinearMap.isSymmetric_iff_inner_map_self_realₓ'. -/
 /-- A linear operator on a complex inner product space is symmetric precisely when
 `⟪T v, v⟫_ℂ` is real for all v.-/
@@ -241,10 +217,7 @@ theorem isSymmetric_iff_inner_map_self_real (T : V →ₗ[ℂ] V) :
 end Complex
 
 /- warning: linear_map.is_symmetric.inner_map_polarization -> LinearMap.IsSymmetric.inner_map_polarization is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) 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(Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T x) y) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (NormedAddGroup.toAddGroup.{u1} 𝕜 (NormedAddCommGroup.toNormedAddGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (NormedAddGroup.toAddGroup.{u1} 𝕜 (NormedAddCommGroup.toNormedAddGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))))) x y)) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))))) x y)) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))) x y)) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))) x y))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (IsROrC.i.{u1} 𝕜 _inst_1) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (IsROrC.i.{u1} 𝕜 _inst_1) y))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (IsROrC.i.{u1} 𝕜 _inst_1) y))))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (IsROrC.i.{u1} 𝕜 _inst_1) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 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(MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E 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_inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (forall (x : E) (y : E), Eq.{succ u2} 𝕜 (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, 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_inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))) x y)) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))) x y))) (HMul.hMul.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHMul.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (IsROrC.I.{u2} 𝕜 _inst_1) (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))))) x (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 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(NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 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_inst_2 _inst_3))))))) (IsROrC.I.{u2} 𝕜 _inst_1) y))) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E 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(NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))))) x (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 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(IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (IsROrC.I.{u2} 𝕜 _inst_1) y))))) (HMul.hMul.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHMul.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (IsROrC.I.{u2} 𝕜 _inst_1) (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))) x (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E 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(InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (IsROrC.I.{u2} 𝕜 _inst_1) y))))) (OfNat.ofNat.{u2} 𝕜 4 (instOfNat.{u2} 𝕜 4 (Semiring.toNatCast.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.inner_map_polarization LinearMap.IsSymmetric.inner_map_polarizationₓ'. -/
 /-- Polarization identity for symmetric linear maps.
 See `inner_map_polarization` for the complex version without the symmetric assumption. -/
@@ -271,10 +244,7 @@ theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymm
 #align linear_map.is_symmetric.inner_map_polarization LinearMap.IsSymmetric.inner_map_polarization
 
 /- warning: linear_map.is_symmetric.inner_map_self_eq_zero -> LinearMap.IsSymmetric.inner_map_self_eq_zero is a dubious translation:
-lean 3 declaration is
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(IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T x) x) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) T (OfNat.ofNat.{u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) 0 (Zero.toOfNat0.{u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.instZeroLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.inner_map_self_eq_zero LinearMap.IsSymmetric.inner_map_self_eq_zeroₓ'. -/
 /-- A symmetric linear map `T` is zero if and only if `⟪T x, x⟫_ℝ = 0` for all `x`.
 See `inner_map_self_eq_zero` for the complex version without the symmetric assumption. -/

3f655f52

bump to nightly-2023-05-26-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

4d5619cc

Diff

@@ -59,42 +59,80 @@ namespace LinearMap
 /-! ### Symmetric operators -/
 
 
+#print LinearMap.IsSymmetric /-
 /-- A (not necessarily bounded) operator on an inner product space is symmetric, if for all
 `x`, `y`, we have `⟪T x, y⟫ = ⟪x, T y⟫`. -/
 def IsSymmetric (T : E →ₗ[𝕜] E) : Prop :=
   ∀ x y, ⟪T x, y⟫ = ⟪x, T y⟫
 #align linear_map.is_symmetric LinearMap.IsSymmetric
+-/
 
 section Real
 
 variable ()
 
+/- warning: linear_map.is_symmetric_iff_sesq_form -> LinearMap.isSymmetric_iff_sesqForm is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] (T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))), Iff (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T) (LinearMap.IsSelfAdjoint.{u1, u2} 𝕜 E (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (starRingEnd.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u1} 𝕜 _inst_1)) (sesqFormOfInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) T)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] (T : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))), Iff (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) (LinearMap.IsSelfAdjoint.{u2, u1} 𝕜 E (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (sesqFormOfInner.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3) T)
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric_iff_sesq_form LinearMap.isSymmetric_iff_sesqFormₓ'. -/
 /-- An operator `T` on an inner product space is symmetric if and only if it is
 `linear_map.is_self_adjoint` with respect to the sesquilinear form given by the inner product. -/
-theorem isSymmetric_iff_sesq_form (T : E →ₗ[𝕜] E) :
+theorem isSymmetric_iff_sesqForm (T : E →ₗ[𝕜] E) :
     T.IsSymmetric ↔ @LinearMap.IsSelfAdjoint 𝕜 E _ _ _ (starRingEnd 𝕜) sesqFormOfInner T :=
   ⟨fun h x y => (h y x).symm, fun h x y => (h y x).symm⟩
-#align linear_map.is_symmetric_iff_sesq_form LinearMap.isSymmetric_iff_sesq_form
+#align linear_map.is_symmetric_iff_sesq_form LinearMap.isSymmetric_iff_sesqForm
 
 end Real
 
+/- warning: linear_map.is_symmetric.conj_inner_sym -> LinearMap.IsSymmetric.conj_inner_sym is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (forall (x : E) (y : E), Eq.{succ u1} 𝕜 (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (fun (_x : RingHom.{u1, u1} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) => 𝕜 -> 𝕜) (RingHom.hasCoeToFun.{u1, u1} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (starRingEnd.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u1} 𝕜 _inst_1)) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T x) y)) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T y) x))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (forall (x : E) (y : E), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (a : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) a) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T x) y)) (FunLike.coe.{succ u2, succ u2, succ u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : 𝕜) => 𝕜) _x) (MulHomClass.toFunLike.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalNonAssocSemiring.toMul.{u2} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (NonUnitalRingHomClass.toMulHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (RingHomClass.toNonUnitalRingHomClass.{u2, u2, u2} (RingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (RingHom.instRingHomClassRingHom.{u2, u2} 𝕜 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (starRingEnd.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toStarRing.{u2} 𝕜 _inst_1)) (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T x) y)) (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) y) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) y) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T y) x))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.conj_inner_sym LinearMap.IsSymmetric.conj_inner_symₓ'. -/
 theorem IsSymmetric.conj_inner_sym {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) (x y : E) :
     conj ⟪T x, y⟫ = ⟪T y, x⟫ := by rw [hT x y, inner_conj_symm]
 #align linear_map.is_symmetric.conj_inner_sym LinearMap.IsSymmetric.conj_inner_sym
 
+/- warning: linear_map.is_symmetric.apply_clm -> LinearMap.IsSymmetric.apply_clm is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (ContinuousLinearMap.LinearMap.coe.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) T)) -> (forall (x : E) (y : E), Eq.{succ u1} 𝕜 (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) T x) y) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) x (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) T y)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 (ContinuousLinearMap.toLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) T)) -> (forall (x : E) (y : E), Eq.{succ u2} 𝕜 (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) x) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) x) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 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_inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))) T x) y) (Inner.inner.{u2, u1} 𝕜 E (InnerProductSpace.toInner.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3) x (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 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_inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 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_inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))) T y)))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.apply_clm LinearMap.IsSymmetric.apply_clmₓ'. -/
 @[simp]
 theorem IsSymmetric.apply_clm {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →ₗ[𝕜] E)) (x y : E) :
     ⟪T x, y⟫ = ⟪x, T y⟫ :=
   hT x y
 #align linear_map.is_symmetric.apply_clm LinearMap.IsSymmetric.apply_clm
 
+/- warning: linear_map.is_symmetric_zero -> LinearMap.isSymmetric_zero is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2], LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 (OfNat.ofNat.{u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) 0 (OfNat.mk.{u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) 0 (Zero.zero.{u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.hasZero.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2], LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 (OfNat.ofNat.{u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) 0 (Zero.toOfNat0.{u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.instZeroLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric_zero LinearMap.isSymmetric_zeroₓ'. -/
 theorem isSymmetric_zero : (0 : E →ₗ[𝕜] E).IsSymmetric := fun x y =>
   (inner_zero_right x : ⟪x, 0⟫ = 0).symm ▸ (inner_zero_left y : ⟪0, y⟫ = 0)
 #align linear_map.is_symmetric_zero LinearMap.isSymmetric_zero
 
+/- warning: linear_map.is_symmetric_id -> LinearMap.isSymmetric_id is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2], LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 (LinearMap.id.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2], LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 (LinearMap.id.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric_id LinearMap.isSymmetric_idₓ'. -/
 theorem isSymmetric_id : (LinearMap.id : E →ₗ[𝕜] E).IsSymmetric := fun x y => rfl
 #align linear_map.is_symmetric_id LinearMap.isSymmetric_id
 
+/- warning: linear_map.is_symmetric.add -> LinearMap.IsSymmetric.add is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))} {S : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 S) -> (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 (HAdd.hAdd.{u2, u2, u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (instHAdd.{u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.hasAdd.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) T S))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))} {S : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 S) -> (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 (HAdd.hAdd.{u1, u1, u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (instHAdd.{u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.instAddLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) T S))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.add LinearMap.IsSymmetric.addₓ'. -/
 theorem IsSymmetric.add {T S : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (hS : S.IsSymmetric) :
     (T + S).IsSymmetric := by
   intro x y
@@ -102,6 +140,12 @@ theorem IsSymmetric.add {T S : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (hS : S.Is
   rfl
 #align linear_map.is_symmetric.add LinearMap.IsSymmetric.add
 
+/- warning: linear_map.is_symmetric.continuous -> LinearMap.IsSymmetric.continuous is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] [_inst_10 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))] {T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (Continuous.{u2, u2} E E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] [_inst_10 : CompleteSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))] {T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (Continuous.{u2, u2} E E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.continuous LinearMap.IsSymmetric.continuousₓ'. -/
 /-- The **Hellinger--Toeplitz theorem**: if a symmetric operator is defined on a complete space,
   then it is automatically continuous. -/
 theorem IsSymmetric.continuous [CompleteSpace E] {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) :
@@ -122,6 +166,12 @@ theorem IsSymmetric.continuous [CompleteSpace E] {T : E →ₗ[𝕜] E} (hT : Is
   exact hu.sub_const _
 #align linear_map.is_symmetric.continuous LinearMap.IsSymmetric.continuous
 
+/- warning: linear_map.is_symmetric.coe_re_apply_inner_self_apply -> LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (HasLiftT.mk.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (CoeTCₓ.coe.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (coeBase.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (ContinuousLinearMap.LinearMap.coe.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) T)) -> (forall (x : E), Eq.{succ u1} 𝕜 ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Real 𝕜 (HasLiftT.mk.{1, succ u1} Real 𝕜 (CoeTCₓ.coe.{1, succ u1} Real 𝕜 (IsROrC.algebraMapCoe.{u1} 𝕜 _inst_1))) (ContinuousLinearMap.reApplyInnerSelf.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T x)) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (ContinuousLinearMap.toFun.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) T x) x))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 (ContinuousLinearMap.toLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) T)) -> (forall (x : E), Eq.{succ u2} 𝕜 (IsROrC.ofReal.{u2} 𝕜 _inst_1 (ContinuousLinearMap.reApplyInnerSelf.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T x)) (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) x) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) x) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => E) _x) (ContinuousMapClass.toFunLike.{u1, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{u1, u2, u2, u1, u1} (ContinuousLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (ContinuousLinearMap.continuousSemilinearMapClass.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))) T x) x))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.coe_re_apply_inner_self_apply LinearMap.IsSymmetric.coe_reApplyInnerSelf_applyₓ'. -/
 /-- For a symmetric operator `T`, the function `λ x, ⟪T x, x⟫` is real-valued. -/
 @[simp]
 theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →ₗ[𝕜] E))
@@ -133,12 +183,24 @@ theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymm
   exact hT.conj_inner_sym x x
 #align linear_map.is_symmetric.coe_re_apply_inner_self_apply LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply
 
+/- warning: linear_map.is_symmetric.restrict_invariant -> LinearMap.IsSymmetric.restrict_invariant is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) 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_inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))} (hV : forall (v : E), (Membership.Mem.{u2, u2} E (Submodule.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (SetLike.hasMem.{u2, u2} (Submodule.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 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(IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T v) V)), LinearMap.IsSymmetric.{u1, u2} 𝕜 (coeSort.{succ u2, succ (succ u2)} (Submodule.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) Type.{u2} (SetLike.hasCoeToSort.{u2, u2} (Submodule.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) E (Submodule.setLike.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))) V) _inst_1 (Submodule.normedAddCommGroup.{u1, u2} 𝕜 E (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) _inst_2 (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) V) (Submodule.innerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 V) (LinearMap.restrict.{u1, u2, u2} 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) T V V hV))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (forall {V : Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))} (hV : forall (v : E), (Membership.mem.{u1, u1} E (Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (Submodule.setLike.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) v V) -> (Membership.mem.{u1, u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) v) (Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (SetLike.instMembership.{u1, u1} (Submodule.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (Submodule.setLike.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 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(Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (Submodule.setLike.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) x V)) _inst_1 (Submodule.normedAddCommGroup.{u2, u1} 𝕜 E (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) _inst_2 (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) V) (Submodule.innerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 V) (LinearMap.restrict.{u2, u1, u1} 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) T V V hV))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariantₓ'. -/
 /-- If a symmetric operator preserves a submodule, its restriction to that submodule is
 symmetric. -/
 theorem IsSymmetric.restrict_invariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) {V : Submodule 𝕜 E}
     (hV : ∀ v ∈ V, T v ∈ V) : IsSymmetric (T.restrict hV) := fun v w => hT v w
 #align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariant
 
+/- warning: linear_map.is_symmetric.restrict_scalars -> LinearMap.IsSymmetric.restrictScalars is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) 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(NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (NormedAlgebra.toAlgebra.{0, u1} Real 𝕜 Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (BoundedSMul.continuousSMul.{0, u1} Real 𝕜 Real.pseudoMetricSpace (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (SubNegMonoid.toAddMonoid.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (SeminormedAddGroup.toAddGroup.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))))) (SMulZeroClass.toHasSmul.{0, u1} Real 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real 𝕜 (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real 𝕜 (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) 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(IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1))))))) (NormedSpace.boundedSMul.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1)))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))) (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{0, u2} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (Real.isScalarTower.{u2, u1} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2) (NormedSpace.toModule.{0, u2} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (BoundedSMul.continuousSMul.{0, u2} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))))) (SMulZeroClass.toHasSmul.{0, u2} Real E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{0, u2} Real E (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real Real.semiring)))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u2} Real E (Semiring.toMonoidWithZero.{0} Real Real.semiring) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{0, u2} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{0, u2} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.boundedSMul.{0, u2} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u2} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))) (T25Space.t2Space.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (T3Space.t25Space.{u2} E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (separated_t3.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (MetricSpace.to_separated.{u2} E (NormedAddCommGroup.toMetricSpace.{u2} E _inst_2))))) 𝕜 (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (NormedAlgebra.toAlgebra.{0, u1} Real 𝕜 Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (BoundedSMul.continuousSMul.{0, u1} Real 𝕜 Real.pseudoMetricSpace (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (MulZeroClass.toHasZero.{0} Real (NonUnitalNonAssocSemiring.toMulZeroClass.{0} Real (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{0} Real (NonAssocRing.toNonUnitalNonAssocRing.{0} Real (Ring.toNonAssocRing.{0} Real (NormedRing.toRing.{0} Real (NormedCommRing.toNormedRing.{0} Real (NormedField.toNormedCommRing.{0} Real Real.normedField)))))))) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (SubNegMonoid.toAddMonoid.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (SeminormedAddGroup.toAddGroup.{u1} 𝕜 (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} 𝕜 (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))))) (SMulZeroClass.toHasSmul.{0, u1} Real 𝕜 (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (SMulWithZero.toSmulZeroClass.{0, u1} Real 𝕜 (MulZeroClass.toHasZero.{0} Real (MulZeroOneClass.toMulZeroClass.{0} Real (MonoidWithZero.toMulZeroOneClass.{0} Real (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring))))) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real 𝕜 (Semiring.toMonoidWithZero.{0} Real (CommSemiring.toSemiring.{0} Real Real.commSemiring)) (AddZeroClass.toHasZero.{u1} 𝕜 (AddMonoid.toAddZeroClass.{u1} 𝕜 (AddCommMonoid.toAddMonoid.{u1} 𝕜 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))) (Module.toMulActionWithZero.{0, u1} Real 𝕜 (CommSemiring.toSemiring.{0} Real Real.commSemiring) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) (Algebra.toModule.{0, u1} Real 𝕜 Real.commSemiring (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u1} Real 𝕜 Real.normedField (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1))))))) (NormedSpace.boundedSMul.{0, u1} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u1} Real Real.normedField 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))) (IsROrC.toNormedAlgebra.{u1} 𝕜 _inst_1)))) (BoundedSMul.continuousSMul.{u1, u2} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)) (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (SeminormedAddGroup.toAddGroup.{u2} E (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))))))) (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (NormedSpace.boundedSMul.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))))) T))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (LinearMap.IsSymmetric.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3) (LinearMap.restrictScalars.{0, u2, u1, u1} Real 𝕜 E E (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (LinearMap.IsScalarTower.compatibleSMul.{u1, u1, 0, u2} E E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) Real 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (Algebra.toSMul.{0, u2} Real 𝕜 Real.instCommSemiringReal (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u2} Real 𝕜 Real.normedField (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1))) (SMulZeroClass.toSMul.{0, u1} Real E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (Real.isScalarTower.{u1, u2} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) (T25Space.t2Space.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (T3Space.t25Space.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (separated_t3.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (MetricSpace.to_separated.{u1} E (NormedAddCommGroup.toMetricSpace.{u1} E _inst_2))))) 𝕜 (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (NormedAlgebra.toAlgebra.{0, u2} Real 𝕜 Real.normedField (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (BoundedSMul.continuousSMul.{0, u2} Real 𝕜 Real.pseudoMetricSpace (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) Real.instZeroReal (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Algebra.toSMul.{0, u2} Real 𝕜 Real.instCommSemiringReal (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u2} Real 𝕜 Real.normedField (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1))) (NormedSpace.boundedSMul.{0, u2} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u2} Real Real.normedField 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1)))) (BoundedSMul.continuousSMul.{u2, u1} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (NormedSpace.boundedSMul.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{0, u1} Real E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E (MonoidWithZero.toZero.{0} Real (Semiring.toMonoidWithZero.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E (Semiring.toMonoidWithZero.{0} Real (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC))))))) (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))) (Module.toMulActionWithZero.{0, u1} Real E (DivisionSemiring.toSemiring.{0} Real (Semifield.toDivisionSemiring.{0} Real (Field.toSemifield.{0} Real (NormedField.toField.{0} Real (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (Real.isScalarTower.{u1, u2} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (BoundedSMul.continuousSMul.{0, u1} Real E Real.pseudoMetricSpace (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{0, u1} Real E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (SMulWithZero.toSMulZeroClass.{0, u1} Real E Real.instZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (MulActionWithZero.toSMulWithZero.{0, u1} Real E Real.instMonoidWithZeroReal (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (Module.toMulActionWithZero.{0, u1} Real E Real.semiring (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{0, u1} Real E (DenselyNormedField.toNormedField.{0} Real (IsROrC.toDenselyNormedField.{0} Real Real.isROrC)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (NormedSpace.boundedSMul.{0, u1} Real E Real.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{0, u1} Real E Real.isROrC _inst_2 (InnerProductSpace.isROrCToReal.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))) (T25Space.t2Space.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (T3Space.t25Space.{u1} E (UniformSpace.toTopologicalSpace.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)))) (separated_t3.{u1} E (PseudoMetricSpace.toUniformSpace.{u1} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (MetricSpace.to_separated.{u1} E (NormedAddCommGroup.toMetricSpace.{u1} E _inst_2))))) 𝕜 (UniformSpace.toTopologicalSpace.{u2} 𝕜 (PseudoMetricSpace.toUniformSpace.{u2} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (NormedAlgebra.toAlgebra.{0, u2} Real 𝕜 Real.normedField (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (BoundedSMul.continuousSMul.{0, u2} Real 𝕜 Real.pseudoMetricSpace (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) Real.instZeroReal (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (Algebra.toSMul.{0, u2} Real 𝕜 Real.instCommSemiringReal (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (NormedAlgebra.toAlgebra.{0, u2} Real 𝕜 Real.normedField (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1))) (NormedSpace.boundedSMul.{0, u2} Real 𝕜 Real.normedField (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} 𝕜 (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} 𝕜 (NormedRing.toNonUnitalNormedRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NormedAlgebra.toNormedSpace'.{0, u2} Real Real.normedField 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))) (IsROrC.toNormedAlgebra.{u2} 𝕜 _inst_1)))) (BoundedSMul.continuousSMul.{u2, u1} 𝕜 E (SeminormedRing.toPseudoMetricSpace.{u2} 𝕜 (SeminormedCommRing.toSeminormedRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2)) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (MonoidWithZero.toZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (SeminormedAddCommGroup.toAddCommGroup.{u1} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2))) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (NormedSpace.boundedSMul.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))) T))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.restrict_scalars LinearMap.IsSymmetric.restrictScalarsₓ'. -/
 theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
     @LinearMap.IsSymmetric ℝ E _ _ (InnerProductSpace.isROrCToReal 𝕜 E)
       (@LinearMap.restrictScalars ℝ 𝕜 _ _ _ _ _ _ (InnerProductSpace.isROrCToReal 𝕜 E).toModule
@@ -150,6 +212,12 @@ section Complex
 
 variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℂ V]
 
+/- warning: linear_map.is_symmetric_iff_inner_map_self_real -> LinearMap.isSymmetric_iff_inner_map_self_real is a dubious translation:
+lean 3 declaration is
+  forall {V : Type.{u1}} [_inst_10 : NormedAddCommGroup.{u1} V] [_inst_11 : InnerProductSpace.{0, u1} Complex V Complex.isROrC _inst_10] (T : LinearMap.{0, 0, u1, u1} Complex Complex (Ring.toSemiring.{0} Complex Complex.ring) (Ring.toSemiring.{0} Complex Complex.ring) (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex (Ring.toSemiring.{0} Complex Complex.ring))) V V (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (NormedSpace.toModule.{0, u1} Complex V Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.isROrC _inst_10 _inst_11)) (NormedSpace.toModule.{0, u1} Complex V Complex.normedField (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.isROrC _inst_10 _inst_11))), Iff (LinearMap.IsSymmetric.{0, u1} Complex V Complex.isROrC _inst_10 _inst_11 T) (forall (v : V), Eq.{1} Complex (coeFn.{1, 1} (RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (fun (_x : RingHom.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) => Complex -> Complex) (RingHom.hasCoeToFun.{0, 0} Complex Complex (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring)) (Semiring.toNonAssocSemiring.{0} Complex (CommSemiring.toSemiring.{0} Complex Complex.commSemiring))) (starRingEnd.{0} Complex Complex.commSemiring Complex.starRing) (Inner.inner.{0, u1} Complex V 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+but is expected to have type
+  forall {V : Type.{u1}} [_inst_10 : NormedAddCommGroup.{u1} V] [_inst_11 : InnerProductSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10] (T : LinearMap.{0, 0, u1, u1} Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) V V (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11))), Iff 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(InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) T v) v)) (Inner.inner.{0, u1} Complex ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V) v) (InnerProductSpace.toInner.{0, u1} Complex ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V) v) Complex.instIsROrCComplex _inst_10 _inst_11) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{0, 0, u1, u1} Complex Complex Complex.instSemiringComplex Complex.instSemiringComplex (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex)) V V (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11))) V (fun (_x : V) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : V) => V) _x) (LinearMap.instFunLikeLinearMap.{0, 0, u1, u1} Complex Complex V V Complex.instSemiringComplex Complex.instSemiringComplex (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (AddCommGroup.toAddCommMonoid.{u1} V (NormedAddCommGroup.toAddCommGroup.{u1} V _inst_10)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (NormedSpace.toModule.{0, u1} Complex V Complex.instNormedFieldComplex (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} V _inst_10) (InnerProductSpace.toNormedSpace.{0, u1} Complex V Complex.instIsROrCComplex _inst_10 _inst_11)) (RingHom.id.{0} Complex (Semiring.toNonAssocSemiring.{0} Complex Complex.instSemiringComplex))) T v) v))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric_iff_inner_map_self_real LinearMap.isSymmetric_iff_inner_map_self_realₓ'. -/
 /-- A linear operator on a complex inner product space is symmetric precisely when
 `⟪T v, v⟫_ℂ` is real for all v.-/
 theorem isSymmetric_iff_inner_map_self_real (T : V →ₗ[ℂ] V) :
@@ -172,6 +240,12 @@ theorem isSymmetric_iff_inner_map_self_real (T : V →ₗ[ℂ] V) :
 
 end Complex
 
+/- warning: linear_map.is_symmetric.inner_map_polarization -> LinearMap.IsSymmetric.inner_map_polarization is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (forall (x : E) (y : E), Eq.{succ u1} 𝕜 (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T x) y) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (NormedDivisionRing.toDivisionRing.{u1} 𝕜 (NormedField.toNormedDivisionRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (NormedAddGroup.toAddGroup.{u1} 𝕜 (NormedAddCommGroup.toNormedAddGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (NormedAddGroup.toAddGroup.{u1} 𝕜 (NormedAddCommGroup.toNormedAddGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))))) x y)) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))))) x y)) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))) x y)) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))) x y))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (IsROrC.i.{u1} 𝕜 _inst_1) 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(NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 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(IsROrC.i.{u1} 𝕜 _inst_1) y))) (HAdd.hAdd.{u2, u2, u2} E E E (instHAdd.{u2} E (AddZeroClass.toHasAdd.{u2} E (AddMonoid.toAddZeroClass.{u2} E (SubNegMonoid.toAddMonoid.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (IsROrC.i.{u1} 𝕜 _inst_1) y))))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (Distrib.toHasMul.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) (IsROrC.i.{u1} 𝕜 _inst_1) (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (IsROrC.i.{u1} 𝕜 _inst_1) y))) (HSub.hSub.{u2, u2, u2} E E E (instHSub.{u2} E (SubNegMonoid.toHasSub.{u2} E (AddGroup.toSubNegMonoid.{u2} E (NormedAddGroup.toAddGroup.{u2} E (NormedAddCommGroup.toNormedAddGroup.{u2} E _inst_2))))) x (SMul.smul.{u1, u2} 𝕜 E (SMulZeroClass.toHasSmul.{u1, u2} 𝕜 E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (SMulWithZero.toSmulZeroClass.{u1, u2} 𝕜 E (MulZeroClass.toHasZero.{u1} 𝕜 (MulZeroOneClass.toMulZeroClass.{u1} 𝕜 (MonoidWithZero.toMulZeroOneClass.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 𝕜 E (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (SeminormedAddCommGroup.toAddCommGroup.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2))) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)))))) (IsROrC.i.{u1} 𝕜 _inst_1) y))))) (OfNat.ofNat.{u1} 𝕜 4 (OfNat.mk.{u1} 𝕜 4 (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (bit0.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))) (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (forall (x : E) (y : E), Eq.{succ u2} 𝕜 (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 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(HDiv.hDiv.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHDiv.{u2} 𝕜 (Field.toDiv.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))) (HAdd.hAdd.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHAdd.{u2} 𝕜 (Distrib.toAdd.{u2} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))))) (HSub.hSub.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHSub.{u2} 𝕜 (Ring.toSub.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (HSub.hSub.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHSub.{u2} 𝕜 (Ring.toSub.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 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(IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 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(AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))) x y)) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E 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(DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))) x y)) (HSub.hSub.{u1, u1, u1} E E E (instHSub.{u1} E (SubNegMonoid.toSub.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))) x y))) (HMul.hMul.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHMul.{u2} 𝕜 (NonUnitalNonAssocRing.toMul.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 (NormedField.toNormedCommRing.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) (IsROrC.I.{u2} 𝕜 _inst_1) (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))))) x (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 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(NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} 𝕜 E (Semiring.toMonoidWithZero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 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_inst_2 _inst_3))))))) (IsROrC.I.{u2} 𝕜 _inst_1) y))) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))))) x (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} 𝕜 E (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 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(Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (IsROrC.I.{u2} 𝕜 _inst_1) y))) (HAdd.hAdd.{u1, u1, u1} E E E (instHAdd.{u1} E (AddZeroClass.toAdd.{u1} E (AddMonoid.toAddZeroClass.{u1} E (SubNegMonoid.toAddMonoid.{u1} E (AddGroup.toSubNegMonoid.{u1} E (NormedAddGroup.toAddGroup.{u1} E (NormedAddCommGroup.toNormedAddGroup.{u1} E _inst_2))))))) x (HSMul.hSMul.{u2, u1, u1} 𝕜 E E (instHSMul.{u2, u1} 𝕜 E (SMulZeroClass.toSMul.{u2, u1} 𝕜 E (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E 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(IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (NegZeroClass.toZero.{u1} E (SubNegZeroMonoid.toNegZeroClass.{u1} E (SubtractionMonoid.toSubNegZeroMonoid.{u1} E (SubtractionCommMonoid.toSubtractionMonoid.{u1} E (AddCommGroup.toDivisionAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} 𝕜 E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (IsROrC.I.{u2} 𝕜 _inst_1) y))))) (HMul.hMul.{u2, u2, u2} 𝕜 𝕜 𝕜 (instHMul.{u2} 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(InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))))))) (IsROrC.I.{u2} 𝕜 _inst_1) y))))) (OfNat.ofNat.{u2} 𝕜 4 (instOfNat.{u2} 𝕜 4 (Semiring.toNatCast.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))))))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.inner_map_polarization LinearMap.IsSymmetric.inner_map_polarizationₓ'. -/
 /-- Polarization identity for symmetric linear maps.
 See `inner_map_polarization` for the complex version without the symmetric assumption. -/
 theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (x y : E) :
@@ -196,6 +270,12 @@ theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymm
     ring
 #align linear_map.is_symmetric.inner_map_polarization LinearMap.IsSymmetric.inner_map_polarization
 
+/- warning: linear_map.is_symmetric.inner_map_self_eq_zero -> LinearMap.IsSymmetric.inner_map_self_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} [_inst_1 : IsROrC.{u1} 𝕜] [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : InnerProductSpace.{u1, u2} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (Iff (forall (x : E), Eq.{succ u1} 𝕜 (Inner.inner.{u1, u2} 𝕜 E (InnerProductSpace.toHasInner.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (fun (_x : LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) => E -> E) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))) T x) x) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))))))))) (Eq.{succ u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) T (OfNat.ofNat.{u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) 0 (OfNat.mk.{u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) 0 (Zero.zero.{u2} (LinearMap.{u1, u1, u2, u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.hasZero.{u1, u1, u2, u2} 𝕜 𝕜 E E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u1, u2} 𝕜 E (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) (InnerProductSpace.toNormedSpace.{u1, u2} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (DenselyNormedField.toNormedField.{u1} 𝕜 (IsROrC.toDenselyNormedField.{u1} 𝕜 _inst_1))))))))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} [_inst_1 : IsROrC.{u2} 𝕜] [_inst_2 : NormedAddCommGroup.{u1} E] [_inst_3 : InnerProductSpace.{u2, u1} 𝕜 E _inst_1 _inst_2] {T : LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))}, (LinearMap.IsSymmetric.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3 T) -> (Iff (forall (x : E), Eq.{succ u2} 𝕜 (Inner.inner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) (InnerProductSpace.toInner.{u2, u1} 𝕜 ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) x) _inst_1 _inst_2 _inst_3) (FunLike.coe.{succ u1, succ u1, succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => E) _x) (LinearMap.instFunLikeLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1))))))))) T x) x) (OfNat.ofNat.{u2} 𝕜 0 (Zero.toOfNat0.{u2} 𝕜 (CommMonoidWithZero.toZero.{u2} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u2} 𝕜 (Semifield.toCommGroupWithZero.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))) (Eq.{succ u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) T (OfNat.ofNat.{u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) 0 (Zero.toOfNat0.{u1} (LinearMap.{u2, u2, u1, u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))) E E (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3))) (LinearMap.instZeroLinearMap.{u2, u2, u1, u1} 𝕜 𝕜 E E (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (AddCommGroup.toAddCommMonoid.{u1} E (NormedAddCommGroup.toAddCommGroup.{u1} E _inst_2)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (NormedSpace.toModule.{u2, u1} 𝕜 E (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} E _inst_2) (InnerProductSpace.toNormedSpace.{u2, u1} 𝕜 E _inst_1 _inst_2 _inst_3)) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 (NormedField.toField.{u2} 𝕜 (DenselyNormedField.toNormedField.{u2} 𝕜 (IsROrC.toDenselyNormedField.{u2} 𝕜 _inst_1)))))))))))))
+Case conversion may be inaccurate. Consider using '#align linear_map.is_symmetric.inner_map_self_eq_zero LinearMap.IsSymmetric.inner_map_self_eq_zeroₓ'. -/
 /-- A symmetric linear map `T` is zero if and only if `⟪T x, x⟫_ℝ = 0` for all `x`.
 See `inner_map_self_eq_zero` for the complex version without the symmetric assumption. -/
 theorem IsSymmetric.inner_map_self_eq_zero {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :

3f655f52

bump to nightly-2023-05-25-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

e9c63ad2

Diff

@@ -88,12 +88,12 @@ theorem IsSymmetric.apply_clm {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →
   hT x y
 #align linear_map.is_symmetric.apply_clm LinearMap.IsSymmetric.apply_clm
 
-theorem isSymmetricZero : (0 : E →ₗ[𝕜] E).IsSymmetric := fun x y =>
+theorem isSymmetric_zero : (0 : E →ₗ[𝕜] E).IsSymmetric := fun x y =>
   (inner_zero_right x : ⟪x, 0⟫ = 0).symm ▸ (inner_zero_left y : ⟪0, y⟫ = 0)
-#align linear_map.is_symmetric_zero LinearMap.isSymmetricZero
+#align linear_map.is_symmetric_zero LinearMap.isSymmetric_zero
 
-theorem isSymmetricId : (LinearMap.id : E →ₗ[𝕜] E).IsSymmetric := fun x y => rfl
-#align linear_map.is_symmetric_id LinearMap.isSymmetricId
+theorem isSymmetric_id : (LinearMap.id : E →ₗ[𝕜] E).IsSymmetric := fun x y => rfl
+#align linear_map.is_symmetric_id LinearMap.isSymmetric_id
 
 theorem IsSymmetric.add {T S : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (hS : S.IsSymmetric) :
     (T + S).IsSymmetric := by
@@ -135,9 +135,9 @@ theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymm
 
 /-- If a symmetric operator preserves a submodule, its restriction to that submodule is
 symmetric. -/
-theorem IsSymmetric.restrictInvariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) {V : Submodule 𝕜 E}
+theorem IsSymmetric.restrict_invariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) {V : Submodule 𝕜 E}
     (hV : ∀ v ∈ V, T v ∈ V) : IsSymmetric (T.restrict hV) := fun v w => hT v w
-#align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrictInvariant
+#align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariant
 
 theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
     @LinearMap.IsSymmetric ℝ E _ _ (InnerProductSpace.isROrCToReal 𝕜 E)

3f655f52

bump to nightly-2023-05-12-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

489c7f8c

Diff

@@ -88,12 +88,12 @@ theorem IsSymmetric.apply_clm {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →
   hT x y
 #align linear_map.is_symmetric.apply_clm LinearMap.IsSymmetric.apply_clm
 
-theorem isSymmetric_zero : (0 : E →ₗ[𝕜] E).IsSymmetric := fun x y =>
+theorem isSymmetricZero : (0 : E →ₗ[𝕜] E).IsSymmetric := fun x y =>
   (inner_zero_right x : ⟪x, 0⟫ = 0).symm ▸ (inner_zero_left y : ⟪0, y⟫ = 0)
-#align linear_map.is_symmetric_zero LinearMap.isSymmetric_zero
+#align linear_map.is_symmetric_zero LinearMap.isSymmetricZero
 
-theorem isSymmetric_id : (LinearMap.id : E →ₗ[𝕜] E).IsSymmetric := fun x y => rfl
-#align linear_map.is_symmetric_id LinearMap.isSymmetric_id
+theorem isSymmetricId : (LinearMap.id : E →ₗ[𝕜] E).IsSymmetric := fun x y => rfl
+#align linear_map.is_symmetric_id LinearMap.isSymmetricId
 
 theorem IsSymmetric.add {T S : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (hS : S.IsSymmetric) :
     (T + S).IsSymmetric := by
@@ -135,9 +135,9 @@ theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymm
 
 /-- If a symmetric operator preserves a submodule, its restriction to that submodule is
 symmetric. -/
-theorem IsSymmetric.restrict_invariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) {V : Submodule 𝕜 E}
+theorem IsSymmetric.restrictInvariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) {V : Submodule 𝕜 E}
     (hV : ∀ v ∈ V, T v ∈ V) : IsSymmetric (T.restrict hV) := fun v w => hT v w
-#align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariant
+#align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrictInvariant
 
 theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
     @LinearMap.IsSymmetric ℝ E _ _ (InnerProductSpace.isROrCToReal 𝕜 E)
@@ -191,7 +191,7 @@ theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymm
       simp_rw [h, MulZeroClass.mul_zero, add_zero]
       norm_cast
   · simp_rw [map_add, map_sub, inner_add_left, inner_add_right, inner_sub_left, inner_sub_right,
-      LinearMap.map_smul, inner_smul_left, inner_smul_right, IsROrC.conj_i, mul_add, mul_sub,
+      LinearMap.map_smul, inner_smul_left, inner_smul_right, IsROrC.conj_I, mul_add, mul_sub,
       sub_sub, ← mul_assoc, mul_neg, h, neg_neg, one_mul, neg_one_mul]
     ring
 #align linear_map.is_symmetric.inner_map_polarization LinearMap.IsSymmetric.inner_map_polarization

3f655f52

bump to nightly-2023-05-09-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

6a26eca8

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.symmetric
-! leanprover-community/mathlib commit caa58cbf5bfb7f81ccbaca4e8b8ac4bc2b39cc1c
+! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -186,7 +186,7 @@ theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymm
     suffices (re ⟪T y, x⟫ : 𝕜) = ⟪T y, x⟫
       by
       rw [conj_eq_iff_re.mpr this]
-      ring_nf
+      ring
     · rw [← re_add_im ⟪T y, x⟫]
       simp_rw [h, MulZeroClass.mul_zero, add_zero]
       norm_cast

caa58cbf

bump to nightly-2023-05-04-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa

047afb6f

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.symmetric
-! leanprover-community/mathlib commit 23b80727b34e571e2e3bd8e8b720820cb215e880
+! leanprover-community/mathlib commit caa58cbf5bfb7f81ccbaca4e8b8ac4bc2b39cc1c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -129,7 +129,7 @@ theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymm
   by
   rsuffices ⟨r, hr⟩ : ∃ r : ℝ, ⟪T x, x⟫ = r
   · simp [hr, T.re_apply_inner_self_apply]
-  rw [← eq_conj_iff_real]
+  rw [← conj_eq_iff_real]
   exact hT.conj_inner_sym x x
 #align linear_map.is_symmetric.coe_re_apply_inner_self_apply LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply
 
@@ -185,7 +185,7 @@ theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymm
       inner_add_right, inner_sub_left, inner_sub_right, hT x, ← inner_conj_symm x (T y)]
     suffices (re ⟪T y, x⟫ : 𝕜) = ⟪T y, x⟫
       by
-      rw [eq_conj_iff_re.mpr this]
+      rw [conj_eq_iff_re.mpr this]
       ring_nf
     · rw [← re_add_im ⟪T y, x⟫]
       simp_rw [h, MulZeroClass.mul_zero, add_zero]

23b80727

bump to nightly-2023-04-12-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

d9bb8048

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.symmetric
-! leanprover-community/mathlib commit 36172d6661e181c215108035483dbbeabd62942e
+! leanprover-community/mathlib commit 23b80727b34e571e2e3bd8e8b720820cb215e880
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -198,7 +198,7 @@ theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymm
 
 /-- A symmetric linear map `T` is zero if and only if `⟪T x, x⟫_ℝ = 0` for all `x`.
 See `inner_map_self_eq_zero` for the complex version without the symmetric assumption. -/
-theorem IsSymmetric.inner_map_eq_zero {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
+theorem IsSymmetric.inner_map_self_eq_zero {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
     (∀ x, ⟪T x, x⟫ = 0) ↔ T = 0 :=
   by
   simp_rw [LinearMap.ext_iff, zero_apply]
@@ -206,7 +206,7 @@ theorem IsSymmetric.inner_map_eq_zero {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric
   rw [← @inner_self_eq_zero 𝕜, hT.inner_map_polarization]
   simp_rw [h _]
   ring
-#align linear_map.is_symmetric.inner_map_eq_zero LinearMap.IsSymmetric.inner_map_eq_zero
+#align linear_map.is_symmetric.inner_map_self_eq_zero LinearMap.IsSymmetric.inner_map_self_eq_zero
 
 end LinearMap

36172d66

bump to nightly-2023-04-09-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228

32290448

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.symmetric
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit 36172d6661e181c215108035483dbbeabd62942e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -172,5 +172,41 @@ theorem isSymmetric_iff_inner_map_self_real (T : V →ₗ[ℂ] V) :
 
 end Complex
 
+/-- Polarization identity for symmetric linear maps.
+See `inner_map_polarization` for the complex version without the symmetric assumption. -/
+theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (x y : E) :
+    ⟪T x, y⟫ =
+      (⟪T (x + y), x + y⟫ - ⟪T (x - y), x - y⟫ - i * ⟪T (x + (i : 𝕜) • y), x + (i : 𝕜) • y⟫ +
+          i * ⟪T (x - (i : 𝕜) • y), x - (i : 𝕜) • y⟫) /
+        4 :=
+  by
+  rcases@I_mul_I_ax 𝕜 _ with (h | h)
+  · simp_rw [h, MulZeroClass.zero_mul, sub_zero, add_zero, map_add, map_sub, inner_add_left,
+      inner_add_right, inner_sub_left, inner_sub_right, hT x, ← inner_conj_symm x (T y)]
+    suffices (re ⟪T y, x⟫ : 𝕜) = ⟪T y, x⟫
+      by
+      rw [eq_conj_iff_re.mpr this]
+      ring_nf
+    · rw [← re_add_im ⟪T y, x⟫]
+      simp_rw [h, MulZeroClass.mul_zero, add_zero]
+      norm_cast
+  · simp_rw [map_add, map_sub, inner_add_left, inner_add_right, inner_sub_left, inner_sub_right,
+      LinearMap.map_smul, inner_smul_left, inner_smul_right, IsROrC.conj_i, mul_add, mul_sub,
+      sub_sub, ← mul_assoc, mul_neg, h, neg_neg, one_mul, neg_one_mul]
+    ring
+#align linear_map.is_symmetric.inner_map_polarization LinearMap.IsSymmetric.inner_map_polarization
+
+/-- A symmetric linear map `T` is zero if and only if `⟪T x, x⟫_ℝ = 0` for all `x`.
+See `inner_map_self_eq_zero` for the complex version without the symmetric assumption. -/
+theorem IsSymmetric.inner_map_eq_zero {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
+    (∀ x, ⟪T x, x⟫ = 0) ↔ T = 0 :=
+  by
+  simp_rw [LinearMap.ext_iff, zero_apply]
+  refine' ⟨fun h x => _, fun h => by simp_rw [h, inner_zero_left, forall_const]⟩
+  rw [← @inner_self_eq_zero 𝕜, hT.inner_map_polarization]
+  simp_rw [h _]
+  ring
+#align linear_map.is_symmetric.inner_map_eq_zero LinearMap.IsSymmetric.inner_map_eq_zero
+
 end LinearMap

46b633fd

bump to nightly-2023-03-26-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

ca5de00c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.symmetric
-! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -43,9 +43,13 @@ open ComplexConjugate
 
 variable {𝕜 E E' F G : Type _} [IsROrC 𝕜]
 
-variable [InnerProductSpace 𝕜 E] [InnerProductSpace 𝕜 F] [InnerProductSpace 𝕜 G]
+variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
-variable [InnerProductSpace ℝ E']
+variable [NormedAddCommGroup F] [InnerProductSpace 𝕜 F]
+
+variable [NormedAddCommGroup G] [InnerProductSpace 𝕜 G]
+
+variable [NormedAddCommGroup E'] [InnerProductSpace ℝ E']
 
 -- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
@@ -105,7 +109,7 @@ theorem IsSymmetric.continuous [CompleteSpace E] {T : E →ₗ[𝕜] E} (hT : Is
   by
   -- We prove it by using the closed graph theorem
   refine' T.continuous_of_seq_closed_graph fun u x y hu hTu => _
-  rw [← sub_eq_zero, ← inner_self_eq_zero]
+  rw [← sub_eq_zero, ← @inner_self_eq_zero 𝕜]
   have hlhs : ∀ k : ℕ, ⟪T (u k) - T x, y - T x⟫ = ⟪u k - x, T (y - T x)⟫ :=
     by
     intro k
@@ -136,7 +140,7 @@ theorem IsSymmetric.restrict_invariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric
 #align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariant
 
 theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
-    @LinearMap.IsSymmetric ℝ E _ (InnerProductSpace.isROrCToReal 𝕜 E)
+    @LinearMap.IsSymmetric ℝ E _ _ (InnerProductSpace.isROrCToReal 𝕜 E)
       (@LinearMap.restrictScalars ℝ 𝕜 _ _ _ _ _ _ (InnerProductSpace.isROrCToReal 𝕜 E).toModule
         (InnerProductSpace.isROrCToReal 𝕜 E).toModule _ _ _ T) :=
   fun x y => by simp [hT x y, real_inner_eq_re_inner, LinearMap.coe_restrictScalars]
@@ -144,7 +148,7 @@ theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric)
 
 section Complex
 
-variable {V : Type _} [InnerProductSpace ℂ V]
+variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℂ V]
 
 /-- A linear operator on a complex inner product space is symmetric precisely when
 `⟪T v, v⟫_ℂ` is real for all v.-/

3fc0b254

bump to nightly-2023-03-15-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

4e269297

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
 
 ! This file was ported from Lean 3 source module analysis.inner_product_space.symmetric
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -75,7 +75,7 @@ theorem isSymmetric_iff_sesq_form (T : E →ₗ[𝕜] E) :
 end Real
 
 theorem IsSymmetric.conj_inner_sym {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) (x y : E) :
-    conj ⟪T x, y⟫ = ⟪T y, x⟫ := by rw [hT x y, inner_conj_sym]
+    conj ⟪T x, y⟫ = ⟪T y, x⟫ := by rw [hT x y, inner_conj_symm]
 #align linear_map.is_symmetric.conj_inner_sym LinearMap.IsSymmetric.conj_inner_sym
 
 @[simp]
@@ -85,7 +85,7 @@ theorem IsSymmetric.apply_clm {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →
 #align linear_map.is_symmetric.apply_clm LinearMap.IsSymmetric.apply_clm
 
 theorem isSymmetric_zero : (0 : E →ₗ[𝕜] E).IsSymmetric := fun x y =>
-  (inner_zero_right : ⟪x, 0⟫ = 0).symm ▸ (inner_zero_left : ⟪0, y⟫ = 0)
+  (inner_zero_right x : ⟪x, 0⟫ = 0).symm ▸ (inner_zero_left y : ⟪0, y⟫ = 0)
 #align linear_map.is_symmetric_zero LinearMap.isSymmetric_zero
 
 theorem isSymmetric_id : (LinearMap.id : E →ₗ[𝕜] E).IsSymmetric := fun x y => rfl
@@ -112,7 +112,7 @@ theorem IsSymmetric.continuous [CompleteSpace E] {T : E →ₗ[𝕜] E} (hT : Is
     rw [← T.map_sub, hT]
   refine' tendsto_nhds_unique ((hTu.sub_const _).inner tendsto_const_nhds) _
   simp_rw [hlhs]
-  rw [← @inner_zero_left 𝕜 E _ _ (T (y - T x))]
+  rw [← inner_zero_left (T (y - T x))]
   refine' Filter.Tendsto.inner _ tendsto_const_nhds
   rw [← sub_self x]
   exact hu.sub_const _
@@ -155,7 +155,7 @@ theorem isSymmetric_iff_inner_map_self_real (T : V →ₗ[ℂ] V) :
   · intro hT v
     apply is_symmetric.conj_inner_sym hT
   · intro h x y
-    nth_rw 2 [← inner_conj_sym]
+    nth_rw 2 [← inner_conj_symm]
     nth_rw 2 [inner_map_polarization]
     simp only [starRingEnd_apply, star_div', star_sub, star_add, star_mul]
     simp only [← starRingEnd_apply]

70fd9563

bump to nightly-2023-03-13-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

66e1e587

Diff

@@ -84,12 +84,12 @@ theorem IsSymmetric.apply_clm {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →
   hT x y
 #align linear_map.is_symmetric.apply_clm LinearMap.IsSymmetric.apply_clm
 
-theorem isSymmetricZero : (0 : E →ₗ[𝕜] E).IsSymmetric := fun x y =>
+theorem isSymmetric_zero : (0 : E →ₗ[𝕜] E).IsSymmetric := fun x y =>
   (inner_zero_right : ⟪x, 0⟫ = 0).symm ▸ (inner_zero_left : ⟪0, y⟫ = 0)
-#align linear_map.is_symmetric_zero LinearMap.isSymmetricZero
+#align linear_map.is_symmetric_zero LinearMap.isSymmetric_zero
 
-theorem isSymmetricId : (LinearMap.id : E →ₗ[𝕜] E).IsSymmetric := fun x y => rfl
-#align linear_map.is_symmetric_id LinearMap.isSymmetricId
+theorem isSymmetric_id : (LinearMap.id : E →ₗ[𝕜] E).IsSymmetric := fun x y => rfl
+#align linear_map.is_symmetric_id LinearMap.isSymmetric_id
 
 theorem IsSymmetric.add {T S : E →ₗ[𝕜] E} (hT : T.IsSymmetric) (hS : S.IsSymmetric) :
     (T + S).IsSymmetric := by
@@ -131,9 +131,9 @@ theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymm
 
 /-- If a symmetric operator preserves a submodule, its restriction to that submodule is
 symmetric. -/
-theorem IsSymmetric.restrictInvariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) {V : Submodule 𝕜 E}
+theorem IsSymmetric.restrict_invariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric T) {V : Submodule 𝕜 E}
     (hV : ∀ v ∈ V, T v ∈ V) : IsSymmetric (T.restrict hV) := fun v w => hT v w
-#align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrictInvariant
+#align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariant
 
 theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
     @LinearMap.IsSymmetric ℝ E _ (InnerProductSpace.isROrCToReal 𝕜 E)

70fd9563

bump to nightly-2023-03-10-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

24f14899

Diff

@@ -159,8 +159,8 @@ theorem isSymmetric_iff_inner_map_self_real (T : V →ₗ[ℂ] V) :
     nth_rw 2 [inner_map_polarization]
     simp only [starRingEnd_apply, star_div', star_sub, star_add, star_mul]
     simp only [← starRingEnd_apply]
-    rw [h (x + y), h (x - y), h (x + Complex.i • y), h (x - Complex.i • y)]
-    simp only [Complex.conj_i]
+    rw [h (x + y), h (x - y), h (x + Complex.I • y), h (x - Complex.I • y)]
+    simp only [Complex.conj_I]
     rw [inner_map_polarization']
     norm_num
     ring

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

3f655f52

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -138,7 +138,7 @@ section Complex
 variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V]
 
 /-- A linear operator on a complex inner product space is symmetric precisely when
-`⟪T v, v⟫_ℂ` is real for all v.-/
+`⟪T v, v⟫_ℂ` is real for all v. -/
 theorem isSymmetric_iff_inner_map_self_real (T : V →ₗ[ℂ] V) :
     IsSymmetric T ↔ ∀ v : V, conj ⟪T v, v⟫_ℂ = ⟪T v, v⟫_ℂ := by
   constructor

3f655f52

chore: Rename IsROrC to RCLike (#10819)

IsROrC contains data, which goes against the expectation that classes prefixed with Is are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC to RCLike.

43618f93

Diff

@@ -34,11 +34,11 @@ self-adjoint, symmetric
 -/
 
 
-open IsROrC
+open RCLike
 
 open ComplexConjugate
 
-variable {𝕜 E E' F G : Type*} [IsROrC 𝕜]
+variable {𝕜 E E' F G : Type*} [RCLike 𝕜]
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 variable [NormedAddCommGroup F] [InnerProductSpace 𝕜 F]
 variable [NormedAddCommGroup G] [InnerProductSpace 𝕜 G]
@@ -127,9 +127,9 @@ theorem IsSymmetric.restrict_invariant {T : E →ₗ[𝕜] E} (hT : IsSymmetric
 #align linear_map.is_symmetric.restrict_invariant LinearMap.IsSymmetric.restrict_invariant
 
 theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric) :
-    @LinearMap.IsSymmetric ℝ E _ _ (InnerProductSpace.isROrCToReal 𝕜 E)
-      (@LinearMap.restrictScalars ℝ 𝕜 _ _ _ _ _ _ (InnerProductSpace.isROrCToReal 𝕜 E).toModule
-        (InnerProductSpace.isROrCToReal 𝕜 E).toModule _ _ _ T) :=
+    @LinearMap.IsSymmetric ℝ E _ _ (InnerProductSpace.rclikeToReal 𝕜 E)
+      (@LinearMap.restrictScalars ℝ 𝕜 _ _ _ _ _ _ (InnerProductSpace.rclikeToReal 𝕜 E).toModule
+        (InnerProductSpace.rclikeToReal 𝕜 E).toModule _ _ _ T) :=
   fun x y => by simp [hT x y, real_inner_eq_re_inner, LinearMap.coe_restrictScalars ℝ]
 #align linear_map.is_symmetric.restrict_scalars LinearMap.IsSymmetric.restrictScalars
 
@@ -175,7 +175,7 @@ theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymm
       simp_rw [h, mul_zero, add_zero]
       norm_cast
   · simp_rw [map_add, map_sub, inner_add_left, inner_add_right, inner_sub_left, inner_sub_right,
-      LinearMap.map_smul, inner_smul_left, inner_smul_right, IsROrC.conj_I, mul_add, mul_sub,
+      LinearMap.map_smul, inner_smul_left, inner_smul_right, RCLike.conj_I, mul_add, mul_sub,
       sub_sub, ← mul_assoc, mul_neg, h, neg_neg, one_mul, neg_one_mul]
     ring
 #align linear_map.is_symmetric.inner_map_polarization LinearMap.IsSymmetric.inner_map_polarization

3f655f52

chore(*): remove empty lines between variable statements (#11418)

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)

75c86f04

Diff

@@ -39,13 +39,9 @@ open IsROrC
 open ComplexConjugate
 
 variable {𝕜 E E' F G : Type*} [IsROrC 𝕜]
-
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
-
 variable [NormedAddCommGroup F] [InnerProductSpace 𝕜 F]
-
 variable [NormedAddCommGroup G] [InnerProductSpace 𝕜 G]
-
 variable [NormedAddCommGroup E'] [InnerProductSpace ℝ E']
 
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y

3f655f52

refactor(LinearAlgebra/SesquilinearForm): Sesquilinear Maps (#9312)

Some of the concepts in LinearAlgebra/SesquilinearForm can be generalised from Sesquilinear Forms to Sesquilinear Maps with little or no impact on the rest of Mathlib. This PR makes those generalisations.

Further generalisations are likely possible, but the scope of this PR is to only consider changes which do not require non-trivial modifications to other parts of Mathlib, or other sections in SesquilinearForm.lean. Further changes can be considered in subsequent PRs if desired.

Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com>

d5ec07c1

Diff

@@ -66,7 +66,7 @@ section Real
 /-- An operator `T` on an inner product space is symmetric if and only if it is
 `LinearMap.IsSelfAdjoint` with respect to the sesquilinear form given by the inner product. -/
 theorem isSymmetric_iff_sesqForm (T : E →ₗ[𝕜] E) :
-    T.IsSymmetric ↔ @LinearMap.IsSelfAdjoint 𝕜 E _ _ _ (starRingEnd 𝕜) sesqFormOfInner T :=
+    T.IsSymmetric ↔ LinearMap.IsSelfAdjoint (R := 𝕜) (M := E) sesqFormOfInner T :=
   ⟨fun h x y => (h y x).symm, fun h x y => (h y x).symm⟩
 #align linear_map.is_symmetric_iff_sesq_form LinearMap.isSymmetric_iff_sesqForm

3f655f52

chore: fix some cases in names (#7469)

And fix some names in comments where this revealed issues

be0d066c

Diff

@@ -25,7 +25,7 @@ symmetric, if for all `x`, `y`, we have `⟪T x, y⟫ = ⟪x, T y⟫`
 
 ## Main statements
 
-* `is_symmetric.continuous`: if a symmetric operator is defined on a complete space, then
+* `IsSymmetric.continuous`: if a symmetric operator is defined on a complete space, then
   it is automatically continuous.
 
 ## Tags

3f655f52

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -170,13 +170,13 @@ theorem IsSymmetric.inner_map_polarization {T : E →ₗ[𝕜] E} (hT : T.IsSymm
           I * ⟪T (x - (I : 𝕜) • y), x - (I : 𝕜) • y⟫) /
         4 := by
   rcases@I_mul_I_ax 𝕜 _ with (h | h)
-  · simp_rw [h, MulZeroClass.zero_mul, sub_zero, add_zero, map_add, map_sub, inner_add_left,
+  · simp_rw [h, zero_mul, sub_zero, add_zero, map_add, map_sub, inner_add_left,
       inner_add_right, inner_sub_left, inner_sub_right, hT x, ← inner_conj_symm x (T y)]
     suffices (re ⟪T y, x⟫ : 𝕜) = ⟪T y, x⟫ by
       rw [conj_eq_iff_re.mpr this]
       ring
     · rw [← re_add_im ⟪T y, x⟫]
-      simp_rw [h, MulZeroClass.mul_zero, add_zero]
+      simp_rw [h, mul_zero, add_zero]
       norm_cast
   · simp_rw [map_add, map_sub, inner_add_left, inner_add_right, inner_sub_left, inner_sub_right,
       LinearMap.map_smul, inner_smul_left, inner_smul_right, IsROrC.conj_I, mul_add, mul_sub,

3f655f52

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -38,7 +38,7 @@ open IsROrC
 
 open ComplexConjugate
 
-variable {𝕜 E E' F G : Type _} [IsROrC 𝕜]
+variable {𝕜 E E' F G : Type*} [IsROrC 𝕜]
 
 variable [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
@@ -139,7 +139,7 @@ theorem IsSymmetric.restrictScalars {T : E →ₗ[𝕜] E} (hT : T.IsSymmetric)
 
 section Complex
 
-variable {V : Type _} [NormedAddCommGroup V] [InnerProductSpace ℂ V]
+variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V]
 
 /-- A linear operator on a complex inner product space is symmetric precisely when
 `⟪T v, v⟫_ℂ` is real for all v.-/

3f655f52

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Anatole Dedecker. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
-
-! This file was ported from Lean 3 source module analysis.inner_product_space.symmetric
-! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.InnerProductSpace.Basic
 import Mathlib.Analysis.NormedSpace.Banach
 import Mathlib.LinearAlgebra.SesquilinearForm
 
+#align_import analysis.inner_product_space.symmetric from "leanprover-community/mathlib"@"3f655f5297b030a87d641ad4e825af8d9679eb0b"
+
 /-!
 # Symmetric linear maps in an inner product space

3f655f52

chore: convert lambda in docs to fun (#5045)

Found with git grep -n "λ [a-zA-Z_ ]*,"

1164cf04

Diff

@@ -117,7 +117,7 @@ theorem IsSymmetric.continuous [CompleteSpace E] {T : E →ₗ[𝕜] E} (hT : Is
   exact hu.sub_const _
 #align linear_map.is_symmetric.continuous LinearMap.IsSymmetric.continuous
 
-/-- For a symmetric operator `T`, the function `λ x, ⟪T x, x⟫` is real-valued. -/
+/-- For a symmetric operator `T`, the function `fun x ↦ ⟪T x, x⟫` is real-valued. -/
 @[simp]
 theorem IsSymmetric.coe_reApplyInnerSelf_apply {T : E →L[𝕜] E} (hT : IsSymmetric (T : E →ₗ[𝕜] E))
     (x : E) : (T.reApplyInnerSelf x : 𝕜) = ⟪T x, x⟫ := by

3f655f52

feat: port Analysis.InnerProductSpace.Symmetric (#4367)

Co-authored-by: Moritz Doll <moritz.doll@googlemail.com>

4bdcb8df

`analysis.inner_product_space.symmetric` ⟷ `Mathlib.Analysis.InnerProductSpace.Symmetric`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 781

analysis.inner_product_space.symmetric ⟷ Mathlib.Analysis.InnerProductSpace.Symmetric

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 781

`analysis.inner_product_space.symmetric` ⟷ `Mathlib.Analysis.InnerProductSpace.Symmetric`