analysis.locally_convex.polar | Mathlib porting status

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

bcfa7268

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

25a9423c

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 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Kalle Kytölä
 -/
-import Mathbin.Analysis.Normed.Field.Basic
-import Mathbin.LinearAlgebra.SesquilinearForm
-import Mathbin.Topology.Algebra.Module.WeakDual
+import Analysis.Normed.Field.Basic
+import LinearAlgebra.SesquilinearForm
+import Topology.Algebra.Module.WeakDual
 
 #align_import analysis.locally_convex.polar from "leanprover-community/mathlib"@"25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e"

25a9423c

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 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Kalle Kytölä
-
-! This file was ported from Lean 3 source module analysis.locally_convex.polar
-! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Normed.Field.Basic
 import Mathbin.LinearAlgebra.SesquilinearForm
 import Mathbin.Topology.Algebra.Module.WeakDual
 
+#align_import analysis.locally_convex.polar from "leanprover-community/mathlib"@"25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e"
+
 /-!
 # Polar set

25a9423c

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -65,23 +65,32 @@ def polar (s : Set E) : Set F :=
 #align linear_map.polar LinearMap.polar
 -/
 
+#print LinearMap.polar_mem_iff /-
 theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   Iff.rfl
 #align linear_map.polar_mem_iff LinearMap.polar_mem_iff
+-/
 
+#print LinearMap.polar_mem /-
 theorem polar_mem (s : Set E) (y : F) (hy : y ∈ B.polar s) : ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   hy
 #align linear_map.polar_mem LinearMap.polar_mem
+-/
 
+#print LinearMap.zero_mem_polar /-
 @[simp]
 theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
   simp only [map_zero, norm_zero, zero_le_one]
 #align linear_map.zero_mem_polar LinearMap.zero_mem_polar
+-/
 
+#print LinearMap.polar_eq_iInter /-
 theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, {y : F | ‖B x y‖ ≤ 1} := by ext;
   simp only [polar_mem_iff, Set.mem_iInter, Set.mem_setOf_eq]
 #align linear_map.polar_eq_Inter LinearMap.polar_eq_iInter
+-/
 
+#print LinearMap.polar_gc /-
 /-- The map `B.polar : set E → set F` forms an order-reversing Galois connection with
 `B.flip.polar : set F → set E`. We use `order_dual.to_dual` and `order_dual.of_dual` to express
 that `polar` is order-reversing. -/
@@ -89,26 +98,36 @@ theorem polar_gc :
     GaloisConnection (OrderDual.toDual ∘ B.polar) (B.flip.polar ∘ OrderDual.ofDual) := fun s t =>
   ⟨fun h _ hx _ hy => h hy _ hx, fun h _ hx _ hy => h hy _ hx⟩
 #align linear_map.polar_gc LinearMap.polar_gc
+-/
 
+#print LinearMap.polar_iUnion /-
 @[simp]
 theorem polar_iUnion {ι} {s : ι → Set E} : B.polar (⋃ i, s i) = ⋂ i, B.polar (s i) :=
   B.polar_gc.l_iSup
 #align linear_map.polar_Union LinearMap.polar_iUnion
+-/
 
+#print LinearMap.polar_union /-
 @[simp]
 theorem polar_union {s t : Set E} : B.polar (s ∪ t) = B.polar s ∩ B.polar t :=
   B.polar_gc.l_sup
 #align linear_map.polar_union LinearMap.polar_union
+-/
 
+#print LinearMap.polar_antitone /-
 theorem polar_antitone : Antitone (B.polar : Set E → Set F) :=
   B.polar_gc.monotone_l
 #align linear_map.polar_antitone LinearMap.polar_antitone
+-/
 
+#print LinearMap.polar_empty /-
 @[simp]
 theorem polar_empty : B.polar ∅ = Set.univ :=
   B.polar_gc.l_bot
 #align linear_map.polar_empty LinearMap.polar_empty
+-/
 
+#print LinearMap.polar_zero /-
 @[simp]
 theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
   by
@@ -116,11 +135,15 @@ theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
   rw [set.mem_singleton_iff.mp hx, map_zero, LinearMap.zero_apply, norm_zero]
   exact zero_le_one
 #align linear_map.polar_zero LinearMap.polar_zero
+-/
 
+#print LinearMap.subset_bipolar /-
 theorem subset_bipolar (s : Set E) : s ⊆ B.flip.polar (B.polar s) := fun x hx y hy => by
   rw [B.flip_apply]; exact hy x hx
 #align linear_map.subset_bipolar LinearMap.subset_bipolar
+-/
 
+#print LinearMap.tripolar_eq_polar /-
 @[simp]
 theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.polar s :=
   by
@@ -128,7 +151,9 @@ theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.p
   convert subset_bipolar B.flip (B.polar s)
   exact B.flip_flip.symm
 #align linear_map.tripolar_eq_polar LinearMap.tripolar_eq_polar
+-/
 
+#print LinearMap.polar_weak_closed /-
 /-- The polar set is closed in the weak topology induced by `B.flip`. -/
 theorem polar_weak_closed (s : Set E) : is_closed[WeakBilin.topologicalSpace B.flip] (B.polar s) :=
   by
@@ -136,6 +161,7 @@ theorem polar_weak_closed (s : Set E) : is_closed[WeakBilin.topologicalSpace B.f
   refine' isClosed_iInter fun x => isClosed_iInter fun _ => _
   exact isClosed_le (WeakBilin.eval_continuous B.flip x).norm continuous_const
 #align linear_map.polar_weak_closed LinearMap.polar_weak_closed
+-/
 
 end NormedRing
 
@@ -147,6 +173,7 @@ variable [Module 𝕜 E] [Module 𝕜 F]
 
 variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)
 
+#print LinearMap.polar_univ /-
 theorem polar_univ (h : SeparatingRight B) : B.polar Set.univ = {(0 : F)} :=
   by
   rw [Set.eq_singleton_iff_unique_mem]
@@ -160,6 +187,7 @@ theorem polar_univ (h : SeparatingRight B) : B.polar Set.univ = {(0 : F)} :=
     _ ≤ ε * 1 := (mul_le_mul hcε.le (hy _ trivial) (norm_nonneg _) hε.le)
     _ = ε := mul_one _
 #align linear_map.polar_univ LinearMap.polar_univ
+-/
 
 end NontriviallyNormedField

25a9423c

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -159,7 +159,6 @@ theorem polar_univ (h : SeparatingRight B) : B.polar Set.univ = {(0 : F)} :=
         mul_inv_cancel_left₀ hc.ne']
     _ ≤ ε * 1 := (mul_le_mul hcε.le (hy _ trivial) (norm_nonneg _) hε.le)
     _ = ε := mul_one _
-    
 #align linear_map.polar_univ LinearMap.polar_univ
 
 end NontriviallyNormedField

25a9423c

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -61,7 +61,7 @@ variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)
 /-- The (absolute) polar of `s : set E` is given by the set of all `y : F` such that `‖B x y‖ ≤ 1`
 for all `x ∈ s`.-/
 def polar (s : Set E) : Set F :=
-  { y : F | ∀ x ∈ s, ‖B x y‖ ≤ 1 }
+  {y : F | ∀ x ∈ s, ‖B x y‖ ≤ 1}
 #align linear_map.polar LinearMap.polar
 -/
 
@@ -78,7 +78,7 @@ theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
   simp only [map_zero, norm_zero, zero_le_one]
 #align linear_map.zero_mem_polar LinearMap.zero_mem_polar
 
-theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } := by ext;
+theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, {y : F | ‖B x y‖ ≤ 1} := by ext;
   simp only [polar_mem_iff, Set.mem_iInter, Set.mem_setOf_eq]
 #align linear_map.polar_eq_Inter LinearMap.polar_eq_iInter

25a9423c

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -45,7 +45,7 @@ polar
 
 variable {𝕜 E F : Type _}
 
-open Topology
+open scoped Topology
 
 namespace LinearMap

25a9423c

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -65,41 +65,23 @@ def polar (s : Set E) : Set F :=
 #align linear_map.polar LinearMap.polar
 -/
 
-/- warning: linear_map.polar_mem_iff -> LinearMap.polar_mem_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem_iff LinearMap.polar_mem_iffₓ'. -/
 theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   Iff.rfl
 #align linear_map.polar_mem_iff LinearMap.polar_mem_iff
 
-/- warning: linear_map.polar_mem -> LinearMap.polar_mem is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem LinearMap.polar_memₓ'. -/
 theorem polar_mem (s : Set E) (y : F) (hy : y ∈ B.polar s) : ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   hy
 #align linear_map.polar_mem LinearMap.polar_mem
 
-/- warning: linear_map.zero_mem_polar -> LinearMap.zero_mem_polar is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) (OfNat.ofNat.{u3} F 0 (OfNat.mk.{u3} F 0 (Zero.zero.{u3} F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3)))))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E), Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
-Case conversion may be inaccurate. Consider using '#align linear_map.zero_mem_polar LinearMap.zero_mem_polarₓ'. -/
 @[simp]
 theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
   simp only [map_zero, norm_zero, zero_le_one]
 #align linear_map.zero_mem_polar LinearMap.zero_mem_polar
 
-/- warning: linear_map.polar_eq_Inter -> LinearMap.polar_eq_iInter is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_eq_Inter LinearMap.polar_eq_iInterₓ'. -/
 theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } := by ext;
   simp only [polar_mem_iff, Set.mem_iInter, Set.mem_setOf_eq]
 #align linear_map.polar_eq_Inter LinearMap.polar_eq_iInter
 
-/- warning: linear_map.polar_gc -> LinearMap.polar_gc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_gc LinearMap.polar_gcₓ'. -/
 /-- The map `B.polar : set E → set F` forms an order-reversing Galois connection with
 `B.flip.polar : set F → set E`. We use `order_dual.to_dual` and `order_dual.of_dual` to express
 that `polar` is order-reversing. -/
@@ -108,52 +90,25 @@ theorem polar_gc :
   ⟨fun h _ hx _ hy => h hy _ hx, fun h _ hx _ hy => h hy _ hx⟩
 #align linear_map.polar_gc LinearMap.polar_gc
 
-/- warning: linear_map.polar_Union -> LinearMap.polar_iUnion is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u2} E)}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.iUnion.{u2, u4} E ι (fun (i : ι) => s i))) (Set.iInter.{u3, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u3} E)}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.iUnion.{u3, u4} E ι (fun (i : ι) => s i))) (Set.iInter.{u2, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_Union LinearMap.polar_iUnionₓ'. -/
 @[simp]
 theorem polar_iUnion {ι} {s : ι → Set E} : B.polar (⋃ i, s i) = ⋂ i, B.polar (s i) :=
   B.polar_gc.l_iSup
 #align linear_map.polar_Union LinearMap.polar_iUnion
 
-/- warning: linear_map.polar_union -> LinearMap.polar_union is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E} {t : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) s t)) (Inter.inter.{u3} (Set.{u3} F) (Set.hasInter.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B t))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {s : Set.{u3} E} {t : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Union.union.{u3} (Set.{u3} E) (Set.instUnionSet.{u3} E) s t)) (Inter.inter.{u2} (Set.{u2} F) (Set.instInterSet.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B t))
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_union LinearMap.polar_unionₓ'. -/
 @[simp]
 theorem polar_union {s t : Set E} : B.polar (s ∪ t) = B.polar s ∩ B.polar t :=
   B.polar_gc.l_sup
 #align linear_map.polar_union LinearMap.polar_union
 
-/- warning: linear_map.polar_antitone -> LinearMap.polar_antitone is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_antitone LinearMap.polar_antitoneₓ'. -/
 theorem polar_antitone : Antitone (B.polar : Set E → Set F) :=
   B.polar_gc.monotone_l
 #align linear_map.polar_antitone LinearMap.polar_antitone
 
-/- warning: linear_map.polar_empty -> LinearMap.polar_empty is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (EmptyCollection.emptyCollection.{u2} (Set.{u2} E) (Set.hasEmptyc.{u2} E))) (Set.univ.{u3} F)
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (EmptyCollection.emptyCollection.{u1} (Set.{u1} E) (Set.instEmptyCollectionSet.{u1} E))) (Set.univ.{u3} F)
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_empty LinearMap.polar_emptyₓ'. -/
 @[simp]
 theorem polar_empty : B.polar ∅ = Set.univ :=
   B.polar_gc.l_bot
 #align linear_map.polar_empty LinearMap.polar_empty
 
-/- warning: linear_map.polar_zero -> LinearMap.polar_zero is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))))))) (Set.univ.{u3} F)
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)))))) (Set.univ.{u3} F)
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_zero LinearMap.polar_zeroₓ'. -/
 @[simp]
 theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
   by
@@ -162,16 +117,10 @@ theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
   exact zero_le_one
 #align linear_map.polar_zero LinearMap.polar_zero
 
-/- warning: linear_map.subset_bipolar -> LinearMap.subset_bipolar is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.subset_bipolar LinearMap.subset_bipolarₓ'. -/
 theorem subset_bipolar (s : Set E) : s ⊆ B.flip.polar (B.polar s) := fun x hx y hy => by
   rw [B.flip_apply]; exact hy x hx
 #align linear_map.subset_bipolar LinearMap.subset_bipolar
 
-/- warning: linear_map.tripolar_eq_polar -> LinearMap.tripolar_eq_polar is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.tripolar_eq_polar LinearMap.tripolar_eq_polarₓ'. -/
 @[simp]
 theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.polar s :=
   by
@@ -180,9 +129,6 @@ theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.p
   exact B.flip_flip.symm
 #align linear_map.tripolar_eq_polar LinearMap.tripolar_eq_polar
 
-/- warning: linear_map.polar_weak_closed -> LinearMap.polar_weak_closed is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_weak_closed LinearMap.polar_weak_closedₓ'. -/
 /-- The polar set is closed in the weak topology induced by `B.flip`. -/
 theorem polar_weak_closed (s : Set E) : is_closed[WeakBilin.topologicalSpace B.flip] (B.polar s) :=
   by
@@ -201,9 +147,6 @@ variable [Module 𝕜 E] [Module 𝕜 F]
 
 variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)
 
-/- warning: linear_map.polar_univ -> LinearMap.polar_univ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_univ LinearMap.polar_univₓ'. -/
 theorem polar_univ (h : SeparatingRight B) : B.polar Set.univ = {(0 : F)} :=
   by
   rw [Set.eq_singleton_iff_unique_mem]

25a9423c

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -93,9 +93,7 @@ theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
 /- warning: linear_map.polar_eq_Inter -> LinearMap.polar_eq_iInter is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_eq_Inter LinearMap.polar_eq_iInterₓ'. -/
-theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } :=
-  by
-  ext
+theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } := by ext;
   simp only [polar_mem_iff, Set.mem_iInter, Set.mem_setOf_eq]
 #align linear_map.polar_eq_Inter LinearMap.polar_eq_iInter
 
@@ -167,10 +165,8 @@ theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
 /- warning: linear_map.subset_bipolar -> LinearMap.subset_bipolar is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.subset_bipolar LinearMap.subset_bipolarₓ'. -/
-theorem subset_bipolar (s : Set E) : s ⊆ B.flip.polar (B.polar s) := fun x hx y hy =>
-  by
-  rw [B.flip_apply]
-  exact hy x hx
+theorem subset_bipolar (s : Set E) : s ⊆ B.flip.polar (B.polar s) := fun x hx y hy => by
+  rw [B.flip_apply]; exact hy x hx
 #align linear_map.subset_bipolar LinearMap.subset_bipolar
 
 /- warning: linear_map.tripolar_eq_polar -> LinearMap.tripolar_eq_polar is a dubious translation:

25a9423c

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -66,20 +66,14 @@ def polar (s : Set E) : Set F :=
 -/
 
 /- warning: linear_map.polar_mem_iff -> LinearMap.polar_mem_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), Iff (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), Iff (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem_iff LinearMap.polar_mem_iffₓ'. -/
 theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   Iff.rfl
 #align linear_map.polar_mem_iff LinearMap.polar_mem_iff
 
 /- warning: linear_map.polar_mem -> LinearMap.polar_mem is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem LinearMap.polar_memₓ'. -/
 theorem polar_mem (s : Set E) (y : F) (hy : y ∈ B.polar s) : ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   hy
@@ -97,10 +91,7 @@ theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
 #align linear_map.zero_mem_polar LinearMap.zero_mem_polar
 
 /- warning: linear_map.polar_eq_Inter -> LinearMap.polar_eq_iInter is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.iInter.{u3, succ u2} F E (fun (x : E) => Set.iInter.{u3, 0} F (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) => setOf.{u3} F (fun (y : F) => LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.iInter.{u2, succ u3} F E (fun (x : E) => Set.iInter.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_eq_Inter LinearMap.polar_eq_iInterₓ'. -/
 theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } :=
   by
@@ -109,10 +100,7 @@ theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x
 #align linear_map.polar_eq_Inter LinearMap.polar_eq_iInter
 
 /- warning: linear_map.polar_gc -> LinearMap.polar_gc is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), GaloisConnection.{u2, u3} (Set.{u2} E) (OrderDual.{u3} (Set.{u3} F)) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E))))))) (OrderDual.preorder.{u3} (Set.{u3} F) (PartialOrder.toPreorder.{u3} (Set.{u3} F) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} F) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} F) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} F) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} F) (Set.completeBooleanAlgebra.{u3} F)))))))) (Function.comp.{succ u2, succ u3, succ u3} (Set.{u2} E) (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F)) (coeFn.{succ u3, succ u3} (Equiv.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) (fun (_x : Equiv.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) => (Set.{u3} F) -> (OrderDual.{u3} (Set.{u3} F))) (Equiv.hasCoeToFun.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) (OrderDual.toDual.{u3} (Set.{u3} F))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F) (Set.{u2} E) (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (coeFn.{succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) (fun (_x : Equiv.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) => (OrderDual.{u3} (Set.{u3} F)) -> (Set.{u3} F)) (Equiv.hasCoeToFun.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) (OrderDual.ofDual.{u3} (Set.{u3} F))))
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))), GaloisConnection.{u3, u2} (Set.{u3} E) (OrderDual.{u2} (Set.{u2} F)) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (OrderDual.preorder.{u2} (Set.{u2} F) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F)))))))) (Function.comp.{succ u3, succ u2, succ u2} (Set.{u3} E) (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (Set.{u2} F) (fun (_x : Set.{u2} F) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Set.{u2} F) => OrderDual.{u2} (Set.{u2} F)) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (OrderDual.toDual.{u2} (Set.{u2} F))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F) (Set.{u3} E) (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) B)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.{u2} (Set.{u2} F)) (fun (_x : OrderDual.{u2} (Set.{u2} F)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u2} (Set.{u2} F)) => Set.{u2} F) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.ofDual.{u2} (Set.{u2} F))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_gc LinearMap.polar_gcₓ'. -/
 /-- The map `B.polar : set E → set F` forms an order-reversing Galois connection with
 `B.flip.polar : set F → set E`. We use `order_dual.to_dual` and `order_dual.of_dual` to express
@@ -145,10 +133,7 @@ theorem polar_union {s t : Set E} : B.polar (s ∪ t) = B.polar s ∩ B.polar t
 #align linear_map.polar_union LinearMap.polar_union
 
 /- warning: linear_map.polar_antitone -> LinearMap.polar_antitone is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Antitone.{u2, u3} (Set.{u2} E) (Set.{u3} F) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} F) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} F) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} F) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} F) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} F) (Set.completeBooleanAlgebra.{u3} F))))))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))), Antitone.{u3, u2} (Set.{u3} E) (Set.{u2} F) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F))))))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_antitone LinearMap.polar_antitoneₓ'. -/
 theorem polar_antitone : Antitone (B.polar : Set E → Set F) :=
   B.polar_gc.monotone_l
@@ -180,10 +165,7 @@ theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
 #align linear_map.polar_zero LinearMap.polar_zero
 
 /- warning: linear_map.subset_bipolar -> LinearMap.subset_bipolar is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))
-but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {F : Type.{u1}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u2, u3} 𝕜 E (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u2, u1} 𝕜 F (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u2, u2, u3, max u2 u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) E (LinearMap.{u2, u2, u1, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u1, u2} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))))))) (s : Set.{u3} E), HasSubset.Subset.{u3} (Set.{u3} E) (Set.instHasSubsetSet.{u3} E) s (LinearMap.polar.{u2, u1, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u2, u2, u2, u2, u3, u1, u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) B) (LinearMap.polar.{u2, u3, u1} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.subset_bipolar LinearMap.subset_bipolarₓ'. -/
 theorem subset_bipolar (s : Set E) : s ⊆ B.flip.polar (B.polar s) := fun x hx y hy =>
   by
@@ -192,10 +174,7 @@ theorem subset_bipolar (s : Set E) : s ⊆ B.flip.polar (B.polar s) := fun x hx
 #align linear_map.subset_bipolar LinearMap.subset_bipolar
 
 /- warning: linear_map.tripolar_eq_polar -> LinearMap.tripolar_eq_polar is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E), Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) B) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.tripolar_eq_polar LinearMap.tripolar_eq_polarₓ'. -/
 @[simp]
 theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.polar s :=
@@ -206,10 +185,7 @@ theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.p
 #align linear_map.tripolar_eq_polar LinearMap.tripolar_eq_polar
 
 /- warning: linear_map.polar_weak_closed -> LinearMap.polar_weak_closed is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), IsClosed.{u3} (WeakBilin.{u1, u3, u2} 𝕜 F E (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (WeakBilin.topologicalSpace.{u1, u3, u2} 𝕜 F E (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
-but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E), IsClosed.{u2} (WeakBilin.{u1, u2, u3} 𝕜 F E (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) B)) (WeakBilin.instTopologicalSpace.{u1, u2, u3} 𝕜 F E (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) B)) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_weak_closed LinearMap.polar_weak_closedₓ'. -/
 /-- The polar set is closed in the weak topology induced by `B.flip`. -/
 theorem polar_weak_closed (s : Set E) : is_closed[WeakBilin.topologicalSpace B.flip] (B.polar s) :=
@@ -230,10 +206,7 @@ variable [Module 𝕜 E] [Module 𝕜 F]
 variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)
 
 /- warning: linear_map.polar_univ -> LinearMap.polar_univ is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))), (LinearMap.SeparatingRight.{u1, u1, u1, u2, u3} 𝕜 𝕜 𝕜 E F (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_2 _inst_4 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_3 _inst_5 (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) B) -> (Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 B (Set.univ.{u2} E)) (Singleton.singleton.{u3, u3} F (Set.{u3} F) (Set.hasSingleton.{u3} F) (OfNat.ofNat.{u3} F 0 (OfNat.mk.{u3} F 0 (Zero.zero.{u3} F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))))))))
-but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {F : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_2] [_inst_5 : Module.{u3, u1} 𝕜 F (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3] (B : LinearMap.{u3, u3, u2, max u3 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) E (LinearMap.{u3, u3, u1, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u3, u3, u1, u3} 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} 𝕜 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (smulCommClass_self.{u3, u3} 𝕜 𝕜 (CommRing.toCommMonoid.{u3} 𝕜 (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (MulActionWithZero.toMulAction.{u3, u3} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (MonoidWithZero.toMulActionWithZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))))))), (LinearMap.SeparatingRight.{u3, u3, u3, u2, u1} 𝕜 𝕜 𝕜 E F (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_2 _inst_4 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_3 _inst_5 (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) B) -> (Eq.{succ u1} (Set.{u1} F) (LinearMap.polar.{u3, u2, u1} 𝕜 E F (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 B (Set.univ.{u2} E)) (Singleton.singleton.{u1, u1} F (Set.{u1} F) (Set.instSingletonSet.{u1} F) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (AddMonoid.toZero.{u1} F (AddCommMonoid.toAddMonoid.{u1} F _inst_3))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_univ LinearMap.polar_univₓ'. -/
 theorem polar_univ (h : SeparatingRight B) : B.polar Set.univ = {(0 : F)} :=
   by

25a9423c

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -69,7 +69,7 @@ def polar (s : Set E) : Set F :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), Iff (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), Iff (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), Iff (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem_iff LinearMap.polar_mem_iffₓ'. -/
 theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   Iff.rfl
@@ -79,7 +79,7 @@ theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem LinearMap.polar_memₓ'. -/
 theorem polar_mem (s : Set E) (y : F) (hy : y ∈ B.polar s) : ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   hy
@@ -100,7 +100,7 @@ theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.iInter.{u3, succ u2} F E (fun (x : E) => Set.iInter.{u3, 0} F (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) => setOf.{u3} F (fun (y : F) => LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.iInter.{u2, succ u3} F E (fun (x : E) => Set.iInter.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.iInter.{u2, succ u3} F E (fun (x : E) => Set.iInter.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_eq_Inter LinearMap.polar_eq_iInterₓ'. -/
 theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } :=
   by

25a9423c

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -112,7 +112,7 @@ theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), GaloisConnection.{u2, u3} (Set.{u2} E) (OrderDual.{u3} (Set.{u3} F)) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E))))))) (OrderDual.preorder.{u3} (Set.{u3} F) (PartialOrder.toPreorder.{u3} (Set.{u3} F) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} F) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} F) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} F) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} F) (Set.completeBooleanAlgebra.{u3} F)))))))) (Function.comp.{succ u2, succ u3, succ u3} (Set.{u2} E) (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F)) (coeFn.{succ u3, succ u3} (Equiv.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) (fun (_x : Equiv.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) => (Set.{u3} F) -> (OrderDual.{u3} (Set.{u3} F))) (Equiv.hasCoeToFun.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) (OrderDual.toDual.{u3} (Set.{u3} F))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F) (Set.{u2} E) (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (coeFn.{succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) (fun (_x : Equiv.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) => (OrderDual.{u3} (Set.{u3} F)) -> (Set.{u3} F)) (Equiv.hasCoeToFun.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) (OrderDual.ofDual.{u3} (Set.{u3} F))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))), GaloisConnection.{u3, u2} (Set.{u3} E) (OrderDual.{u2} (Set.{u2} F)) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (OrderDual.preorder.{u2} (Set.{u2} F) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F)))))))) (Function.comp.{succ u3, succ u2, succ u2} (Set.{u3} E) (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (Set.{u2} F) (fun (_x : Set.{u2} F) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.{u2} F) => OrderDual.{u2} (Set.{u2} F)) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (OrderDual.toDual.{u2} (Set.{u2} F))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F) (Set.{u3} E) (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) B)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.{u2} (Set.{u2} F)) (fun (_x : OrderDual.{u2} (Set.{u2} F)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} (Set.{u2} F)) => Set.{u2} F) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.ofDual.{u2} (Set.{u2} F))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))), GaloisConnection.{u3, u2} (Set.{u3} E) (OrderDual.{u2} (Set.{u2} F)) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (OrderDual.preorder.{u2} (Set.{u2} F) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F)))))))) (Function.comp.{succ u3, succ u2, succ u2} (Set.{u3} E) (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (Set.{u2} F) (fun (_x : Set.{u2} F) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Set.{u2} F) => OrderDual.{u2} (Set.{u2} F)) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (OrderDual.toDual.{u2} (Set.{u2} F))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F) (Set.{u3} E) (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) B)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.{u2} (Set.{u2} F)) (fun (_x : OrderDual.{u2} (Set.{u2} F)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : OrderDual.{u2} (Set.{u2} F)) => Set.{u2} F) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.ofDual.{u2} (Set.{u2} F))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_gc LinearMap.polar_gcₓ'. -/
 /-- The map `B.polar : set E → set F` forms an order-reversing Galois connection with
 `B.flip.polar : set F → set E`. We use `order_dual.to_dual` and `order_dual.of_dual` to express

25a9423c

bump to nightly-2023-05-18-03

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

b46e9d53

Diff

@@ -69,7 +69,7 @@ def polar (s : Set E) : Set F :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), Iff (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), Iff (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), Iff (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem_iff LinearMap.polar_mem_iffₓ'. -/
 theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   Iff.rfl
@@ -79,7 +79,7 @@ theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem LinearMap.polar_memₓ'. -/
 theorem polar_mem (s : Set E) (y : F) (hy : y ∈ B.polar s) : ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   hy
@@ -100,7 +100,7 @@ theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.iInter.{u3, succ u2} F E (fun (x : E) => Set.iInter.{u3, 0} F (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) => setOf.{u3} F (fun (y : F) => LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.iInter.{u2, succ u3} F E (fun (x : E) => Set.iInter.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.iInter.{u2, succ u3} F E (fun (x : E) => Set.iInter.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_eq_Inter LinearMap.polar_eq_iInterₓ'. -/
 theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } :=
   by

25a9423c

bump to nightly-2023-05-14-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

d31da313

Diff

@@ -96,17 +96,17 @@ theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
   simp only [map_zero, norm_zero, zero_le_one]
 #align linear_map.zero_mem_polar LinearMap.zero_mem_polar
 
-/- warning: linear_map.polar_eq_Inter -> LinearMap.polar_eq_interᵢ is a dubious translation:
+/- warning: linear_map.polar_eq_Inter -> LinearMap.polar_eq_iInter is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.interᵢ.{u3, succ u2} F E (fun (x : E) => Set.interᵢ.{u3, 0} F (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) => setOf.{u3} F (fun (y : F) => LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.iInter.{u3, succ u2} F E (fun (x : E) => Set.iInter.{u3, 0} F (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) => setOf.{u3} F (fun (y : F) => LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.interᵢ.{u2, succ u3} F E (fun (x : E) => Set.interᵢ.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_eq_Inter LinearMap.polar_eq_interᵢₓ'. -/
-theorem polar_eq_interᵢ {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } :=
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.iInter.{u2, succ u3} F E (fun (x : E) => Set.iInter.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_eq_Inter LinearMap.polar_eq_iInterₓ'. -/
+theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } :=
   by
   ext
-  simp only [polar_mem_iff, Set.mem_interᵢ, Set.mem_setOf_eq]
-#align linear_map.polar_eq_Inter LinearMap.polar_eq_interᵢ
+  simp only [polar_mem_iff, Set.mem_iInter, Set.mem_setOf_eq]
+#align linear_map.polar_eq_Inter LinearMap.polar_eq_iInter
 
 /- warning: linear_map.polar_gc -> LinearMap.polar_gc is a dubious translation:
 lean 3 declaration is
@@ -122,16 +122,16 @@ theorem polar_gc :
   ⟨fun h _ hx _ hy => h hy _ hx, fun h _ hx _ hy => h hy _ hx⟩
 #align linear_map.polar_gc LinearMap.polar_gc
 
-/- warning: linear_map.polar_Union -> LinearMap.polar_unionᵢ is a dubious translation:
+/- warning: linear_map.polar_Union -> LinearMap.polar_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u2} E)}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.unionᵢ.{u2, u4} E ι (fun (i : ι) => s i))) (Set.interᵢ.{u3, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u2} E)}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.iUnion.{u2, u4} E ι (fun (i : ι) => s i))) (Set.iInter.{u3, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u3} E)}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.unionᵢ.{u3, u4} E ι (fun (i : ι) => s i))) (Set.interᵢ.{u2, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
-Case conversion may be inaccurate. Consider using '#align linear_map.polar_Union LinearMap.polar_unionᵢₓ'. -/
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u3} E)}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.iUnion.{u3, u4} E ι (fun (i : ι) => s i))) (Set.iInter.{u2, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_Union LinearMap.polar_iUnionₓ'. -/
 @[simp]
-theorem polar_unionᵢ {ι} {s : ι → Set E} : B.polar (⋃ i, s i) = ⋂ i, B.polar (s i) :=
-  B.polar_gc.l_supᵢ
-#align linear_map.polar_Union LinearMap.polar_unionᵢ
+theorem polar_iUnion {ι} {s : ι → Set E} : B.polar (⋃ i, s i) = ⋂ i, B.polar (s i) :=
+  B.polar_gc.l_iSup
+#align linear_map.polar_Union LinearMap.polar_iUnion
 
 /- warning: linear_map.polar_union -> LinearMap.polar_union is a dubious translation:
 lean 3 declaration is
@@ -215,7 +215,7 @@ Case conversion may be inaccurate. Consider using '#align linear_map.polar_weak_
 theorem polar_weak_closed (s : Set E) : is_closed[WeakBilin.topologicalSpace B.flip] (B.polar s) :=
   by
   rw [polar_eq_Inter]
-  refine' isClosed_interᵢ fun x => isClosed_interᵢ fun _ => _
+  refine' isClosed_iInter fun x => isClosed_iInter fun _ => _
   exact isClosed_le (WeakBilin.eval_continuous B.flip x).norm continuous_const
 #align linear_map.polar_weak_closed LinearMap.polar_weak_closed

25a9423c

bump to nightly-2023-05-08-22

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

63e712c6

Diff

@@ -69,7 +69,7 @@ def polar (s : Set E) : Set F :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), Iff (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E) (y : F), Iff (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), Iff (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem_iff LinearMap.polar_mem_iffₓ'. -/
 theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   Iff.rfl
@@ -79,7 +79,7 @@ theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E) (y : F), (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E) (y : F), (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem LinearMap.polar_memₓ'. -/
 theorem polar_mem (s : Set E) (y : F) (hy : y ∈ B.polar s) : ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   hy
@@ -89,7 +89,7 @@ theorem polar_mem (s : Set E) (y : F) (hy : y ∈ B.polar s) : ∀ x ∈ s, ‖B
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) (OfNat.ofNat.{u3} F 0 (OfNat.mk.{u3} F 0 (Zero.zero.{u3} F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3)))))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E), Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 Case conversion may be inaccurate. Consider using '#align linear_map.zero_mem_polar LinearMap.zero_mem_polarₓ'. -/
 @[simp]
 theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
@@ -100,7 +100,7 @@ theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.interᵢ.{u3, succ u2} F E (fun (x : E) => Set.interᵢ.{u3, 0} F (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) => setOf.{u3} F (fun (y : F) => LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.interᵢ.{u2, succ u3} F E (fun (x : E) => Set.interᵢ.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.interᵢ.{u2, succ u3} F E (fun (x : E) => Set.interᵢ.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_eq_Inter LinearMap.polar_eq_interᵢₓ'. -/
 theorem polar_eq_interᵢ {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } :=
   by
@@ -112,7 +112,7 @@ theorem polar_eq_interᵢ {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), GaloisConnection.{u2, u3} (Set.{u2} E) (OrderDual.{u3} (Set.{u3} F)) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E))))))) (OrderDual.preorder.{u3} (Set.{u3} F) (PartialOrder.toPreorder.{u3} (Set.{u3} F) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} F) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} F) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} F) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} F) (Set.completeBooleanAlgebra.{u3} F)))))))) (Function.comp.{succ u2, succ u3, succ u3} (Set.{u2} E) (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F)) (coeFn.{succ u3, succ u3} (Equiv.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) (fun (_x : Equiv.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) => (Set.{u3} F) -> (OrderDual.{u3} (Set.{u3} F))) (Equiv.hasCoeToFun.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) (OrderDual.toDual.{u3} (Set.{u3} F))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F) (Set.{u2} E) (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (coeFn.{succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) (fun (_x : Equiv.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) => (OrderDual.{u3} (Set.{u3} F)) -> (Set.{u3} F)) (Equiv.hasCoeToFun.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) (OrderDual.ofDual.{u3} (Set.{u3} F))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))), GaloisConnection.{u3, u2} (Set.{u3} E) (OrderDual.{u2} (Set.{u2} F)) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (OrderDual.preorder.{u2} (Set.{u2} F) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F)))))))) (Function.comp.{succ u3, succ u2, succ u2} (Set.{u3} E) (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (Set.{u2} F) (fun (_x : Set.{u2} F) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.{u2} F) => OrderDual.{u2} (Set.{u2} F)) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (OrderDual.toDual.{u2} (Set.{u2} F))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F) (Set.{u3} E) (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.{u2} (Set.{u2} F)) (fun (_x : OrderDual.{u2} (Set.{u2} F)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} (Set.{u2} F)) => Set.{u2} F) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.ofDual.{u2} (Set.{u2} F))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))), GaloisConnection.{u3, u2} (Set.{u3} E) (OrderDual.{u2} (Set.{u2} F)) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (OrderDual.preorder.{u2} (Set.{u2} F) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F)))))))) (Function.comp.{succ u3, succ u2, succ u2} (Set.{u3} E) (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (Set.{u2} F) (fun (_x : Set.{u2} F) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.{u2} F) => OrderDual.{u2} (Set.{u2} F)) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (OrderDual.toDual.{u2} (Set.{u2} F))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F) (Set.{u3} E) (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) B)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.{u2} (Set.{u2} F)) (fun (_x : OrderDual.{u2} (Set.{u2} F)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} (Set.{u2} F)) => Set.{u2} F) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.ofDual.{u2} (Set.{u2} F))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_gc LinearMap.polar_gcₓ'. -/
 /-- The map `B.polar : set E → set F` forms an order-reversing Galois connection with
 `B.flip.polar : set F → set E`. We use `order_dual.to_dual` and `order_dual.of_dual` to express
@@ -126,7 +126,7 @@ theorem polar_gc :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u2} E)}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.unionᵢ.{u2, u4} E ι (fun (i : ι) => s i))) (Set.interᵢ.{u3, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u3} E)}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.unionᵢ.{u3, u4} E ι (fun (i : ι) => s i))) (Set.interᵢ.{u2, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u3} E)}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.unionᵢ.{u3, u4} E ι (fun (i : ι) => s i))) (Set.interᵢ.{u2, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_Union LinearMap.polar_unionᵢₓ'. -/
 @[simp]
 theorem polar_unionᵢ {ι} {s : ι → Set E} : B.polar (⋃ i, s i) = ⋂ i, B.polar (s i) :=
@@ -137,7 +137,7 @@ theorem polar_unionᵢ {ι} {s : ι → Set E} : B.polar (⋃ i, s i) = ⋂ i, B
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E} {t : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) s t)) (Inter.inter.{u3} (Set.{u3} F) (Set.hasInter.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B t))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {s : Set.{u3} E} {t : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Union.union.{u3} (Set.{u3} E) (Set.instUnionSet.{u3} E) s t)) (Inter.inter.{u2} (Set.{u2} F) (Set.instInterSet.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B t))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) {s : Set.{u3} E} {t : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Union.union.{u3} (Set.{u3} E) (Set.instUnionSet.{u3} E) s t)) (Inter.inter.{u2} (Set.{u2} F) (Set.instInterSet.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B t))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_union LinearMap.polar_unionₓ'. -/
 @[simp]
 theorem polar_union {s t : Set E} : B.polar (s ∪ t) = B.polar s ∩ B.polar t :=
@@ -148,7 +148,7 @@ theorem polar_union {s t : Set E} : B.polar (s ∪ t) = B.polar s ∩ B.polar t
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Antitone.{u2, u3} (Set.{u2} E) (Set.{u3} F) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} F) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} F) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} F) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} F) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} F) (Set.completeBooleanAlgebra.{u3} F))))))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))), Antitone.{u3, u2} (Set.{u3} E) (Set.{u2} F) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F))))))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))), Antitone.{u3, u2} (Set.{u3} E) (Set.{u2} F) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F))))))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_antitone LinearMap.polar_antitoneₓ'. -/
 theorem polar_antitone : Antitone (B.polar : Set E → Set F) :=
   B.polar_gc.monotone_l
@@ -158,7 +158,7 @@ theorem polar_antitone : Antitone (B.polar : Set E → Set F) :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (EmptyCollection.emptyCollection.{u2} (Set.{u2} E) (Set.hasEmptyc.{u2} E))) (Set.univ.{u3} F)
 but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (EmptyCollection.emptyCollection.{u1} (Set.{u1} E) (Set.instEmptyCollectionSet.{u1} E))) (Set.univ.{u3} F)
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (EmptyCollection.emptyCollection.{u1} (Set.{u1} E) (Set.instEmptyCollectionSet.{u1} E))) (Set.univ.{u3} F)
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_empty LinearMap.polar_emptyₓ'. -/
 @[simp]
 theorem polar_empty : B.polar ∅ = Set.univ :=
@@ -169,7 +169,7 @@ theorem polar_empty : B.polar ∅ = Set.univ :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))))))) (Set.univ.{u3} F)
 but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)))))) (Set.univ.{u3} F)
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)))))) (Set.univ.{u3} F)
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_zero LinearMap.polar_zeroₓ'. -/
 @[simp]
 theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
@@ -183,7 +183,7 @@ theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))
 but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {F : Type.{u1}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u2, u3} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u1} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u3, max u2 u1} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u1, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u1, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))) (s : Set.{u3} E), HasSubset.Subset.{u3} (Set.{u3} E) (Set.instHasSubsetSet.{u3} E) s (LinearMap.polar.{u2, u1, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u2, u2, u2, u2, u3, u1, u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) B) (LinearMap.polar.{u2, u3, u1} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {F : Type.{u1}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u2, u3} 𝕜 E (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u2, u1} 𝕜 F (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u2, u2, u3, max u2 u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) E (LinearMap.{u2, u2, u1, u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u1, u2} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))))))) (s : Set.{u3} E), HasSubset.Subset.{u3} (Set.{u3} E) (Set.instHasSubsetSet.{u3} E) s (LinearMap.polar.{u2, u1, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u2, u2, u2, u2, u3, u1, u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (Semiring.toModule.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) (RingHom.id.{u2} 𝕜 (Semiring.toNonAssocSemiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1)))))) B) (LinearMap.polar.{u2, u3, u1} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))
 Case conversion may be inaccurate. Consider using '#align linear_map.subset_bipolar LinearMap.subset_bipolarₓ'. -/
 theorem subset_bipolar (s : Set E) : s ⊆ B.flip.polar (B.polar s) := fun x hx y hy =>
   by
@@ -195,7 +195,7 @@ theorem subset_bipolar (s : Set E) : s ⊆ B.flip.polar (B.polar s) := fun x hx
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E), Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) B) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 Case conversion may be inaccurate. Consider using '#align linear_map.tripolar_eq_polar LinearMap.tripolar_eq_polarₓ'. -/
 @[simp]
 theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.polar s :=
@@ -209,7 +209,7 @@ theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.p
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), IsClosed.{u3} (WeakBilin.{u1, u3, u2} 𝕜 F E (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (WeakBilin.topologicalSpace.{u1, u3, u2} 𝕜 F E (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), IsClosed.{u2} (WeakBilin.{u1, u2, u3} 𝕜 F E (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (WeakBilin.instTopologicalSpace.{u1, u2, u3} 𝕜 F E (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))))) (s : Set.{u3} E), IsClosed.{u2} (WeakBilin.{u1, u2, u3} 𝕜 F E (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) B)) (WeakBilin.instTopologicalSpace.{u1, u2, u3} 𝕜 F E (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) B)) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_weak_closed LinearMap.polar_weak_closedₓ'. -/
 /-- The polar set is closed in the weak topology induced by `B.flip`. -/
 theorem polar_weak_closed (s : Set E) : is_closed[WeakBilin.topologicalSpace B.flip] (B.polar s) :=
@@ -233,7 +233,7 @@ variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))), (LinearMap.SeparatingRight.{u1, u1, u1, u2, u3} 𝕜 𝕜 𝕜 E F (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_2 _inst_4 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_3 _inst_5 (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) B) -> (Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 B (Set.univ.{u2} E)) (Singleton.singleton.{u3, u3} F (Set.{u3} F) (Set.hasSingleton.{u3} F) (OfNat.ofNat.{u3} F 0 (OfNat.mk.{u3} F 0 (Zero.zero.{u3} F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))))))))
 but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {F : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_2] [_inst_5 : Module.{u3, u1} 𝕜 F (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3] (B : LinearMap.{u3, u3, u2, max u3 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) E (LinearMap.{u3, u3, u1, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u3, u3, u1, u3} 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} 𝕜 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (smulCommClass_self.{u3, u3} 𝕜 𝕜 (CommRing.toCommMonoid.{u3} 𝕜 (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (MulActionWithZero.toMulAction.{u3, u3} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (MonoidWithZero.toMulActionWithZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))))))), (LinearMap.SeparatingRight.{u3, u3, u3, u2, u1} 𝕜 𝕜 𝕜 E F (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_2 _inst_4 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_3 _inst_5 (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) B) -> (Eq.{succ u1} (Set.{u1} F) (LinearMap.polar.{u3, u2, u1} 𝕜 E F (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 B (Set.univ.{u2} E)) (Singleton.singleton.{u1, u1} F (Set.{u1} F) (Set.instSingletonSet.{u1} F) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (AddMonoid.toZero.{u1} F (AddCommMonoid.toAddMonoid.{u1} F _inst_3))))))
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {F : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_2] [_inst_5 : Module.{u3, u1} 𝕜 F (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3] (B : LinearMap.{u3, u3, u2, max u3 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) E (LinearMap.{u3, u3, u1, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u3, u3, u1, u3} 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} 𝕜 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (smulCommClass_self.{u3, u3} 𝕜 𝕜 (CommRing.toCommMonoid.{u3} 𝕜 (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (MulActionWithZero.toMulAction.{u3, u3} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (MonoidWithZero.toMulActionWithZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))))))), (LinearMap.SeparatingRight.{u3, u3, u3, u2, u1} 𝕜 𝕜 𝕜 E F (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_2 _inst_4 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_3 _inst_5 (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (RingHom.id.{u3} 𝕜 (Semiring.toNonAssocSemiring.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) B) -> (Eq.{succ u1} (Set.{u1} F) (LinearMap.polar.{u3, u2, u1} 𝕜 E F (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 B (Set.univ.{u2} E)) (Singleton.singleton.{u1, u1} F (Set.{u1} F) (Set.instSingletonSet.{u1} F) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (AddMonoid.toZero.{u1} F (AddCommMonoid.toAddMonoid.{u1} F _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_univ LinearMap.polar_univₓ'. -/
 theorem polar_univ (h : SeparatingRight B) : B.polar Set.univ = {(0 : F)} :=
   by

25a9423c

bump to nightly-2023-04-27-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/9b2b58d6b14b895b2f375108e765cb47de71aebd

c8f7a684

Diff

@@ -69,7 +69,7 @@ def polar (s : Set E) : Set F :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), Iff (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E) (y : F), Iff (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E) (y : F), Iff (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem_iff LinearMap.polar_mem_iffₓ'. -/
 theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   Iff.rfl
@@ -79,7 +79,7 @@ theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E) (y : F), (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E) (y : F), (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem LinearMap.polar_memₓ'. -/
 theorem polar_mem (s : Set E) (y : F) (hy : y ∈ B.polar s) : ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   hy
@@ -89,7 +89,7 @@ theorem polar_mem (s : Set E) (y : F) (hy : y ∈ B.polar s) : ∀ x ∈ s, ‖B
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) (OfNat.ofNat.{u3} F 0 (OfNat.mk.{u3} F 0 (Zero.zero.{u3} F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3)))))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 Case conversion may be inaccurate. Consider using '#align linear_map.zero_mem_polar LinearMap.zero_mem_polarₓ'. -/
 @[simp]
 theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
@@ -100,7 +100,7 @@ theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.interᵢ.{u3, succ u2} F E (fun (x : E) => Set.interᵢ.{u3, 0} F (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) => setOf.{u3} F (fun (y : F) => LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.interᵢ.{u2, succ u3} F E (fun (x : E) => Set.interᵢ.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.interᵢ.{u2, succ u3} F E (fun (x : E) => Set.interᵢ.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_eq_Inter LinearMap.polar_eq_interᵢₓ'. -/
 theorem polar_eq_interᵢ {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } :=
   by
@@ -112,7 +112,7 @@ theorem polar_eq_interᵢ {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), GaloisConnection.{u2, u3} (Set.{u2} E) (OrderDual.{u3} (Set.{u3} F)) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E))))))) (OrderDual.preorder.{u3} (Set.{u3} F) (PartialOrder.toPreorder.{u3} (Set.{u3} F) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} F) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} F) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} F) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} F) (Set.completeBooleanAlgebra.{u3} F)))))))) (Function.comp.{succ u2, succ u3, succ u3} (Set.{u2} E) (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F)) (coeFn.{succ u3, succ u3} (Equiv.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) (fun (_x : Equiv.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) => (Set.{u3} F) -> (OrderDual.{u3} (Set.{u3} F))) (Equiv.hasCoeToFun.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) (OrderDual.toDual.{u3} (Set.{u3} F))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F) (Set.{u2} E) (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (coeFn.{succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) (fun (_x : Equiv.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) => (OrderDual.{u3} (Set.{u3} F)) -> (Set.{u3} F)) (Equiv.hasCoeToFun.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) (OrderDual.ofDual.{u3} (Set.{u3} F))))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))), GaloisConnection.{u3, u2} (Set.{u3} E) (OrderDual.{u2} (Set.{u2} F)) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (OrderDual.preorder.{u2} (Set.{u2} F) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F)))))))) (Function.comp.{succ u3, succ u2, succ u2} (Set.{u3} E) (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (Set.{u2} F) (fun (_x : Set.{u2} F) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.{u2} F) => OrderDual.{u2} (Set.{u2} F)) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (OrderDual.toDual.{u2} (Set.{u2} F))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F) (Set.{u3} E) (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.{u2} (Set.{u2} F)) (fun (_x : OrderDual.{u2} (Set.{u2} F)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} (Set.{u2} F)) => Set.{u2} F) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.ofDual.{u2} (Set.{u2} F))))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))), GaloisConnection.{u3, u2} (Set.{u3} E) (OrderDual.{u2} (Set.{u2} F)) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (OrderDual.preorder.{u2} (Set.{u2} F) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F)))))))) (Function.comp.{succ u3, succ u2, succ u2} (Set.{u3} E) (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (Set.{u2} F) (fun (_x : Set.{u2} F) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.{u2} F) => OrderDual.{u2} (Set.{u2} F)) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (OrderDual.toDual.{u2} (Set.{u2} F))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F) (Set.{u3} E) (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.{u2} (Set.{u2} F)) (fun (_x : OrderDual.{u2} (Set.{u2} F)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} (Set.{u2} F)) => Set.{u2} F) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.ofDual.{u2} (Set.{u2} F))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_gc LinearMap.polar_gcₓ'. -/
 /-- The map `B.polar : set E → set F` forms an order-reversing Galois connection with
 `B.flip.polar : set F → set E`. We use `order_dual.to_dual` and `order_dual.of_dual` to express
@@ -126,7 +126,7 @@ theorem polar_gc :
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u2} E)}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.unionᵢ.{u2, u4} E ι (fun (i : ι) => s i))) (Set.interᵢ.{u3, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u3} E)}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.unionᵢ.{u3, u4} E ι (fun (i : ι) => s i))) (Set.interᵢ.{u2, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u3} E)}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.unionᵢ.{u3, u4} E ι (fun (i : ι) => s i))) (Set.interᵢ.{u2, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_Union LinearMap.polar_unionᵢₓ'. -/
 @[simp]
 theorem polar_unionᵢ {ι} {s : ι → Set E} : B.polar (⋃ i, s i) = ⋂ i, B.polar (s i) :=
@@ -137,7 +137,7 @@ theorem polar_unionᵢ {ι} {s : ι → Set E} : B.polar (⋃ i, s i) = ⋂ i, B
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E} {t : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) s t)) (Inter.inter.{u3} (Set.{u3} F) (Set.hasInter.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B t))
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {s : Set.{u3} E} {t : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Union.union.{u3} (Set.{u3} E) (Set.instUnionSet.{u3} E) s t)) (Inter.inter.{u2} (Set.{u2} F) (Set.instInterSet.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B t))
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {s : Set.{u3} E} {t : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Union.union.{u3} (Set.{u3} E) (Set.instUnionSet.{u3} E) s t)) (Inter.inter.{u2} (Set.{u2} F) (Set.instInterSet.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B t))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_union LinearMap.polar_unionₓ'. -/
 @[simp]
 theorem polar_union {s t : Set E} : B.polar (s ∪ t) = B.polar s ∩ B.polar t :=
@@ -148,7 +148,7 @@ theorem polar_union {s t : Set E} : B.polar (s ∪ t) = B.polar s ∩ B.polar t
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Antitone.{u2, u3} (Set.{u2} E) (Set.{u3} F) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} F) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} F) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} F) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} F) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} F) (Set.completeBooleanAlgebra.{u3} F))))))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))), Antitone.{u3, u2} (Set.{u3} E) (Set.{u2} F) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F))))))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))), Antitone.{u3, u2} (Set.{u3} E) (Set.{u2} F) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F))))))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_antitone LinearMap.polar_antitoneₓ'. -/
 theorem polar_antitone : Antitone (B.polar : Set E → Set F) :=
   B.polar_gc.monotone_l
@@ -158,7 +158,7 @@ theorem polar_antitone : Antitone (B.polar : Set E → Set F) :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (EmptyCollection.emptyCollection.{u2} (Set.{u2} E) (Set.hasEmptyc.{u2} E))) (Set.univ.{u3} F)
 but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (EmptyCollection.emptyCollection.{u1} (Set.{u1} E) (Set.instEmptyCollectionSet.{u1} E))) (Set.univ.{u3} F)
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (EmptyCollection.emptyCollection.{u1} (Set.{u1} E) (Set.instEmptyCollectionSet.{u1} E))) (Set.univ.{u3} F)
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_empty LinearMap.polar_emptyₓ'. -/
 @[simp]
 theorem polar_empty : B.polar ∅ = Set.univ :=
@@ -169,7 +169,7 @@ theorem polar_empty : B.polar ∅ = Set.univ :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))))))) (Set.univ.{u3} F)
 but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)))))) (Set.univ.{u3} F)
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)))))) (Set.univ.{u3} F)
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_zero LinearMap.polar_zeroₓ'. -/
 @[simp]
 theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
@@ -183,7 +183,7 @@ theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))
 but is expected to have type
-  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {F : Type.{u1}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u2, u3} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u1} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u3, max u2 u1} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u1, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u1, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))) (s : Set.{u3} E), HasSubset.Subset.{u3} (Set.{u3} E) (Set.instHasSubsetSet.{u3} E) s (LinearMap.polar.{u2, u1, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u2, u2, u2, u2, u3, u1, u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) B) (LinearMap.polar.{u2, u3, u1} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {F : Type.{u1}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u2, u3} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u1} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u3, max u2 u1} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u1, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u1, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))) (s : Set.{u3} E), HasSubset.Subset.{u3} (Set.{u3} E) (Set.instHasSubsetSet.{u3} E) s (LinearMap.polar.{u2, u1, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u2, u2, u2, u2, u3, u1, u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (Semiring.toModule.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) B) (LinearMap.polar.{u2, u3, u1} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))
 Case conversion may be inaccurate. Consider using '#align linear_map.subset_bipolar LinearMap.subset_bipolarₓ'. -/
 theorem subset_bipolar (s : Set E) : s ⊆ B.flip.polar (B.polar s) := fun x hx y hy =>
   by
@@ -195,7 +195,7 @@ theorem subset_bipolar (s : Set E) : s ⊆ B.flip.polar (B.polar s) := fun x hx
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 Case conversion may be inaccurate. Consider using '#align linear_map.tripolar_eq_polar LinearMap.tripolar_eq_polarₓ'. -/
 @[simp]
 theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.polar s :=
@@ -209,7 +209,7 @@ theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.p
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), IsClosed.{u3} (WeakBilin.{u1, u3, u2} 𝕜 F E (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (WeakBilin.topologicalSpace.{u1, u3, u2} 𝕜 F E (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 but is expected to have type
-  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), IsClosed.{u2} (WeakBilin.{u1, u2, u3} 𝕜 F E (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (WeakBilin.instTopologicalSpace.{u1, u2, u3} 𝕜 F E (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), IsClosed.{u2} (WeakBilin.{u1, u2, u3} 𝕜 F E (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (WeakBilin.instTopologicalSpace.{u1, u2, u3} 𝕜 F E (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_weak_closed LinearMap.polar_weak_closedₓ'. -/
 /-- The polar set is closed in the weak topology induced by `B.flip`. -/
 theorem polar_weak_closed (s : Set E) : is_closed[WeakBilin.topologicalSpace B.flip] (B.polar s) :=
@@ -233,7 +233,7 @@ variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)
 lean 3 declaration is
   forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))), (LinearMap.SeparatingRight.{u1, u1, u1, u2, u3} 𝕜 𝕜 𝕜 E F (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_2 _inst_4 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_3 _inst_5 (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) B) -> (Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 B (Set.univ.{u2} E)) (Singleton.singleton.{u3, u3} F (Set.{u3} F) (Set.hasSingleton.{u3} F) (OfNat.ofNat.{u3} F 0 (OfNat.mk.{u3} F 0 (Zero.zero.{u3} F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))))))))
 but is expected to have type
-  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {F : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_2] [_inst_5 : Module.{u3, u1} 𝕜 F (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3] (B : LinearMap.{u3, u3, u2, max u3 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) E (LinearMap.{u3, u3, u1, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRingToEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u3, u3, u1, u3} 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRingToEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} 𝕜 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRingToEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRingToEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))) (smulCommClass_self.{u3, u3} 𝕜 𝕜 (CommRing.toCommMonoid.{u3} 𝕜 (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (MulActionWithZero.toMulAction.{u3, u3} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (MonoidWithZero.toMulActionWithZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))))))), (LinearMap.SeparatingRight.{u3, u3, u3, u2, u1} 𝕜 𝕜 𝕜 E F (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_2 _inst_4 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_3 _inst_5 (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) B) -> (Eq.{succ u1} (Set.{u1} F) (LinearMap.polar.{u3, u2, u1} 𝕜 E F (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 B (Set.univ.{u2} E)) (Singleton.singleton.{u1, u1} F (Set.{u1} F) (Set.instSingletonSet.{u1} F) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (AddMonoid.toZero.{u1} F (AddCommMonoid.toAddMonoid.{u1} F _inst_3))))))
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {F : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_2] [_inst_5 : Module.{u3, u1} 𝕜 F (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3] (B : LinearMap.{u3, u3, u2, max u3 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) E (LinearMap.{u3, u3, u1, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u3, u3, u1, u3} 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} 𝕜 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (Semiring.toModule.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (smulCommClass_self.{u3, u3} 𝕜 𝕜 (CommRing.toCommMonoid.{u3} 𝕜 (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (MulActionWithZero.toMulAction.{u3, u3} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (MonoidWithZero.toMulActionWithZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))))))), (LinearMap.SeparatingRight.{u3, u3, u3, u2, u1} 𝕜 𝕜 𝕜 E F (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_2 _inst_4 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_3 _inst_5 (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) B) -> (Eq.{succ u1} (Set.{u1} F) (LinearMap.polar.{u3, u2, u1} 𝕜 E F (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 B (Set.univ.{u2} E)) (Singleton.singleton.{u1, u1} F (Set.{u1} F) (Set.instSingletonSet.{u1} F) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (AddMonoid.toZero.{u1} F (AddCommMonoid.toAddMonoid.{u1} F _inst_3))))))
 Case conversion may be inaccurate. Consider using '#align linear_map.polar_univ LinearMap.polar_univₓ'. -/
 theorem polar_univ (h : SeparatingRight B) : B.polar Set.univ = {(0 : F)} :=
   by

25a9423c

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, Kalle Kytölä
 
 ! This file was ported from Lean 3 source module analysis.locally_convex.polar
-! leanprover-community/mathlib commit bcfa726826abd57587355b4b5b7e78ad6527b7e4
+! leanprover-community/mathlib commit 25a9423c6b2c8626e91c688bfd6c1d0a986a3e6e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Topology.Algebra.Module.WeakDual
 /-!
 # Polar set
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define the polar set. There are different notions of the polar, we will define the
 *absolute polar*. The advantage over the real polar is that we can define the absolute polar for
 any bilinear form `B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜`, where `𝕜` is a normed commutative ring and

bcfa7268

bump to nightly-2023-04-10-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/e05ead7993520a432bec94ac504842d90707ad63

af46b02d

Diff

@@ -54,31 +54,63 @@ variable [Module 𝕜 E] [Module 𝕜 F]
 
 variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)
 
+#print LinearMap.polar /-
 /-- The (absolute) polar of `s : set E` is given by the set of all `y : F` such that `‖B x y‖ ≤ 1`
 for all `x ∈ s`.-/
 def polar (s : Set E) : Set F :=
   { y : F | ∀ x ∈ s, ‖B x y‖ ≤ 1 }
 #align linear_map.polar LinearMap.polar
+-/
 
+/- warning: linear_map.polar_mem_iff -> LinearMap.polar_mem_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), Iff (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E) (y : F), Iff (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem_iff LinearMap.polar_mem_iffₓ'. -/
 theorem polar_mem_iff (s : Set E) (y : F) : y ∈ B.polar s ↔ ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   Iff.rfl
 #align linear_map.polar_mem_iff LinearMap.polar_mem_iff
 
+/- warning: linear_map.polar_mem -> LinearMap.polar_mem is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E) (y : F), (Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) y (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E) (y : F), (Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) y (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)) -> (forall (x : E), (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_mem LinearMap.polar_memₓ'. -/
 theorem polar_mem (s : Set E) (y : F) (hy : y ∈ B.polar s) : ∀ x ∈ s, ‖B x y‖ ≤ 1 :=
   hy
 #align linear_map.polar_mem LinearMap.polar_mem
 
+/- warning: linear_map.zero_mem_polar -> LinearMap.zero_mem_polar is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), Membership.Mem.{u3, u3} F (Set.{u3} F) (Set.hasMem.{u3} F) (OfNat.ofNat.{u3} F 0 (OfNat.mk.{u3} F 0 (Zero.zero.{u3} F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3)))))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), Membership.mem.{u2, u2} F (Set.{u2} F) (Set.instMembershipSet.{u2} F) (OfNat.ofNat.{u2} F 0 (Zero.toOfNat0.{u2} F (AddMonoid.toZero.{u2} F (AddCommMonoid.toAddMonoid.{u2} F _inst_3)))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+Case conversion may be inaccurate. Consider using '#align linear_map.zero_mem_polar LinearMap.zero_mem_polarₓ'. -/
 @[simp]
 theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
   simp only [map_zero, norm_zero, zero_le_one]
 #align linear_map.zero_mem_polar LinearMap.zero_mem_polar
 
+/- warning: linear_map.polar_eq_Inter -> LinearMap.polar_eq_interᵢ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.interᵢ.{u3, succ u2} F E (fun (x : E) => Set.interᵢ.{u3, 0} F (Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) (fun (H : Membership.Mem.{u2, u2} E (Set.{u2} E) (Set.hasMem.{u2} E) x s) => setOf.{u3} F (fun (y : F) => LE.le.{0} Real Real.hasLe (Norm.norm.{u1} 𝕜 (NormedRing.toHasNorm.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)) (coeFn.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (fun (_x : LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) => F -> 𝕜) (LinearMap.hasCoeToFun.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (fun (_x : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) => E -> (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (LinearMap.hasCoeToFun.{u1, u1, u2, max u3 u1} 𝕜 𝕜 E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {s : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (Set.interᵢ.{u2, succ u3} F E (fun (x : E) => Set.interᵢ.{u2, 0} F (Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) (fun (H : Membership.mem.{u3, u3} E (Set.{u3} E) (Set.instMembershipSet.{u3} E) x s) => setOf.{u2} F (fun (y : F) => LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedRing.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) (NormedCommRing.toNormedRing.{u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) y) _inst_1)) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} ((fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) x) F (fun (_x : F) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : F) => 𝕜) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) (FunLike.coe.{max (max (succ u1) (succ u3)) (succ u2), succ u3, max (succ u1) (succ u2)} (LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) E (fun (_x : E) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : E) => LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) B x) y)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))))
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_eq_Inter LinearMap.polar_eq_interᵢₓ'. -/
 theorem polar_eq_interᵢ {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } :=
   by
   ext
   simp only [polar_mem_iff, Set.mem_interᵢ, Set.mem_setOf_eq]
 #align linear_map.polar_eq_Inter LinearMap.polar_eq_interᵢ
 
+/- warning: linear_map.polar_gc -> LinearMap.polar_gc is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), GaloisConnection.{u2, u3} (Set.{u2} E) (OrderDual.{u3} (Set.{u3} F)) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E))))))) (OrderDual.preorder.{u3} (Set.{u3} F) (PartialOrder.toPreorder.{u3} (Set.{u3} F) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} F) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} F) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} F) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} F) (Set.completeBooleanAlgebra.{u3} F)))))))) (Function.comp.{succ u2, succ u3, succ u3} (Set.{u2} E) (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F)) (coeFn.{succ u3, succ u3} (Equiv.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) (fun (_x : Equiv.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) => (Set.{u3} F) -> (OrderDual.{u3} (Set.{u3} F))) (Equiv.hasCoeToFun.{succ u3, succ u3} (Set.{u3} F) (OrderDual.{u3} (Set.{u3} F))) (OrderDual.toDual.{u3} (Set.{u3} F))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u3, succ u3, succ u2} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F) (Set.{u2} E) (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (coeFn.{succ u3, succ u3} (Equiv.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) (fun (_x : Equiv.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) => (OrderDual.{u3} (Set.{u3} F)) -> (Set.{u3} F)) (Equiv.hasCoeToFun.{succ u3, succ u3} (OrderDual.{u3} (Set.{u3} F)) (Set.{u3} F)) (OrderDual.ofDual.{u3} (Set.{u3} F))))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))), GaloisConnection.{u3, u2} (Set.{u3} E) (OrderDual.{u2} (Set.{u2} F)) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (OrderDual.preorder.{u2} (Set.{u2} F) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F)))))))) (Function.comp.{succ u3, succ u2, succ u2} (Set.{u3} E) (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (Set.{u2} F) (fun (_x : Set.{u2} F) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : Set.{u2} F) => OrderDual.{u2} (Set.{u2} F)) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (Set.{u2} F) (OrderDual.{u2} (Set.{u2} F))) (OrderDual.toDual.{u2} (Set.{u2} F))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)) (Function.comp.{succ u2, succ u2, succ u3} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F) (Set.{u3} E) (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (FunLike.coe.{succ u2, succ u2, succ u2} (Equiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.{u2} (Set.{u2} F)) (fun (_x : OrderDual.{u2} (Set.{u2} F)) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : OrderDual.{u2} (Set.{u2} F)) => Set.{u2} F) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u2} (OrderDual.{u2} (Set.{u2} F)) (Set.{u2} F)) (OrderDual.ofDual.{u2} (Set.{u2} F))))
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_gc LinearMap.polar_gcₓ'. -/
 /-- The map `B.polar : set E → set F` forms an order-reversing Galois connection with
 `B.flip.polar : set F → set E`. We use `order_dual.to_dual` and `order_dual.of_dual` to express
 that `polar` is order-reversing. -/
@@ -87,25 +119,55 @@ theorem polar_gc :
   ⟨fun h _ hx _ hy => h hy _ hx, fun h _ hx _ hy => h hy _ hx⟩
 #align linear_map.polar_gc LinearMap.polar_gc
 
+/- warning: linear_map.polar_Union -> LinearMap.polar_unionᵢ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u2} E)}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.unionᵢ.{u2, u4} E ι (fun (i : ι) => s i))) (Set.interᵢ.{u3, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {ι : Sort.{u4}} {s : ι -> (Set.{u3} E)}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Set.unionᵢ.{u3, u4} E ι (fun (i : ι) => s i))) (Set.interᵢ.{u2, u4} F ι (fun (i : ι) => LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (s i)))
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_Union LinearMap.polar_unionᵢₓ'. -/
 @[simp]
 theorem polar_unionᵢ {ι} {s : ι → Set E} : B.polar (⋃ i, s i) = ⋂ i, B.polar (s i) :=
   B.polar_gc.l_supᵢ
 #align linear_map.polar_Union LinearMap.polar_unionᵢ
 
+/- warning: linear_map.polar_union -> LinearMap.polar_union is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) {s : Set.{u2} E} {t : Set.{u2} E}, Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Union.union.{u2} (Set.{u2} E) (Set.hasUnion.{u2} E) s t)) (Inter.inter.{u3} (Set.{u3} F) (Set.hasInter.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B t))
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) {s : Set.{u3} E} {t : Set.{u3} E}, Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Union.union.{u3} (Set.{u3} E) (Set.instUnionSet.{u3} E) s t)) (Inter.inter.{u2} (Set.{u2} F) (Set.instInterSet.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B t))
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_union LinearMap.polar_unionₓ'. -/
 @[simp]
 theorem polar_union {s t : Set E} : B.polar (s ∪ t) = B.polar s ∩ B.polar t :=
   B.polar_gc.l_sup
 #align linear_map.polar_union LinearMap.polar_union
 
+/- warning: linear_map.polar_antitone -> LinearMap.polar_antitone is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Antitone.{u2, u3} (Set.{u2} E) (Set.{u3} F) (PartialOrder.toPreorder.{u2} (Set.{u2} E) (CompleteSemilatticeInf.toPartialOrder.{u2} (Set.{u2} E) (CompleteLattice.toCompleteSemilatticeInf.{u2} (Set.{u2} E) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} E) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} E) (Set.completeBooleanAlgebra.{u2} E))))))) (PartialOrder.toPreorder.{u3} (Set.{u3} F) (CompleteSemilatticeInf.toPartialOrder.{u3} (Set.{u3} F) (CompleteLattice.toCompleteSemilatticeInf.{u3} (Set.{u3} F) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} F) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} F) (Set.completeBooleanAlgebra.{u3} F))))))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))), Antitone.{u3, u2} (Set.{u3} E) (Set.{u2} F) (PartialOrder.toPreorder.{u3} (Set.{u3} E) (OmegaCompletePartialOrder.toPartialOrder.{u3} (Set.{u3} E) (CompleteLattice.instOmegaCompletePartialOrder.{u3} (Set.{u3} E) (Order.Coframe.toCompleteLattice.{u3} (Set.{u3} E) (CompleteDistribLattice.toCoframe.{u3} (Set.{u3} E) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u3} (Set.{u3} E) (Set.instCompleteBooleanAlgebraSet.{u3} E))))))) (PartialOrder.toPreorder.{u2} (Set.{u2} F) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} F) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} F) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} F) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} F) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} F) (Set.instCompleteBooleanAlgebraSet.{u2} F))))))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B)
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_antitone LinearMap.polar_antitoneₓ'. -/
 theorem polar_antitone : Antitone (B.polar : Set E → Set F) :=
   B.polar_gc.monotone_l
 #align linear_map.polar_antitone LinearMap.polar_antitone
 
+/- warning: linear_map.polar_empty -> LinearMap.polar_empty is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (EmptyCollection.emptyCollection.{u2} (Set.{u2} E) (Set.hasEmptyc.{u2} E))) (Set.univ.{u3} F)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (EmptyCollection.emptyCollection.{u1} (Set.{u1} E) (Set.instEmptyCollectionSet.{u1} E))) (Set.univ.{u3} F)
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_empty LinearMap.polar_emptyₓ'. -/
 @[simp]
 theorem polar_empty : B.polar ∅ = Set.univ :=
   B.polar_gc.l_bot
 #align linear_map.polar_empty LinearMap.polar_empty
 
+/- warning: linear_map.polar_zero -> LinearMap.polar_zero is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Singleton.singleton.{u2, u2} E (Set.{u2} E) (Set.hasSingleton.{u2} E) (OfNat.ofNat.{u2} E 0 (OfNat.mk.{u2} E 0 (Zero.zero.{u2} E (AddZeroClass.toHasZero.{u2} E (AddMonoid.toAddZeroClass.{u2} E (AddCommMonoid.toAddMonoid.{u2} E _inst_2)))))))) (Set.univ.{u3} F)
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u1}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u1} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u2, u1} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u3} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u1, max u2 u3} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u3, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u3, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u3, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u2, u1, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (Singleton.singleton.{u1, u1} E (Set.{u1} E) (Set.instSingletonSet.{u1} E) (OfNat.ofNat.{u1} E 0 (Zero.toOfNat0.{u1} E (AddMonoid.toZero.{u1} E (AddCommMonoid.toAddMonoid.{u1} E _inst_2)))))) (Set.univ.{u3} F)
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_zero LinearMap.polar_zeroₓ'. -/
 @[simp]
 theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
   by
@@ -114,12 +176,24 @@ theorem polar_zero : B.polar ({0} : Set E) = Set.univ :=
   exact zero_le_one
 #align linear_map.polar_zero LinearMap.polar_zero
 
+/- warning: linear_map.subset_bipolar -> LinearMap.subset_bipolar is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), HasSubset.Subset.{u2} (Set.{u2} E) (Set.hasSubset.{u2} E) s (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {E : Type.{u3}} {F : Type.{u1}} [_inst_1 : NormedCommRing.{u2} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u2, u3} 𝕜 E (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u2, u1} 𝕜 F (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u2, u2, u3, max u2 u1} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) E (LinearMap.{u2, u2, u1, u2} 𝕜 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u2, u2, u1, u2} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u2, u2, u2, u1, u2} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))))) (s : Set.{u3} E), HasSubset.Subset.{u3} (Set.{u3} E) (Set.instHasSubsetSet.{u3} E) s (LinearMap.polar.{u2, u1, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u2, u2, u2, u2, u3, u1, u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u2} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))))) _inst_4 _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))) (smulCommClass_self.{u2, u2} 𝕜 𝕜 (CommRing.toCommMonoid.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u2, u2} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u2} 𝕜 (CommSemiring.toCommMonoidWithZero.{u2} 𝕜 (CommRing.toCommSemiring.{u2} 𝕜 (SeminormedCommRing.toCommRing.{u2} 𝕜 (NormedCommRing.toSeminormedCommRing.{u2} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u2} 𝕜 (Semiring.toMonoidWithZero.{u2} 𝕜 (Ring.toSemiring.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) (RingHom.id.{u2} 𝕜 (NonAssocRing.toNonAssocSemiring.{u2} 𝕜 (Ring.toNonAssocRing.{u2} 𝕜 (NormedRing.toRing.{u2} 𝕜 (NormedCommRing.toNormedRing.{u2} 𝕜 _inst_1))))) B) (LinearMap.polar.{u2, u3, u1} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))
+Case conversion may be inaccurate. Consider using '#align linear_map.subset_bipolar LinearMap.subset_bipolarₓ'. -/
 theorem subset_bipolar (s : Set E) : s ⊆ B.flip.polar (B.polar s) := fun x hx y hy =>
   by
   rw [B.flip_apply]
   exact hy x hx
 #align linear_map.subset_bipolar LinearMap.subset_bipolar
 
+/- warning: linear_map.tripolar_eq_polar -> LinearMap.tripolar_eq_polar is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (LinearMap.polar.{u1, u3, u2} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), Eq.{succ u2} (Set.{u2} F) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B (LinearMap.polar.{u1, u2, u3} 𝕜 F E _inst_1 _inst_3 _inst_2 _inst_5 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s))) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+Case conversion may be inaccurate. Consider using '#align linear_map.tripolar_eq_polar LinearMap.tripolar_eq_polarₓ'. -/
 @[simp]
 theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.polar s :=
   by
@@ -128,6 +202,12 @@ theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.p
   exact B.flip_flip.symm
 #align linear_map.tripolar_eq_polar LinearMap.tripolar_eq_polar
 
+/- warning: linear_map.polar_weak_closed -> LinearMap.polar_weak_closed is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))))) (s : Set.{u2} E), IsClosed.{u3} (WeakBilin.{u1, u3, u2} 𝕜 F E (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (WeakBilin.topologicalSpace.{u1, u3, u2} 𝕜 F E (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSemiNormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u2, u3, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) _inst_4 _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1)))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (LinearMap.polar.{u1, u2, u3} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+but is expected to have type
+  forall {𝕜 : Type.{u1}} {E : Type.{u3}} {F : Type.{u2}} [_inst_1 : NormedCommRing.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u3} E] [_inst_3 : AddCommMonoid.{u2} F] [_inst_4 : Module.{u1, u3} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_2] [_inst_5 : Module.{u1, u2} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3] (B : LinearMap.{u1, u1, u3, max u1 u2} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) E (LinearMap.{u1, u1, u2, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u2, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))))) (s : Set.{u3} E), IsClosed.{u2} (WeakBilin.{u1, u2, u3} 𝕜 F E (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (WeakBilin.instTopologicalSpace.{u1, u2, u3} 𝕜 F E (UniformSpace.toTopologicalSpace.{u1} 𝕜 (PseudoMetricSpace.toUniformSpace.{u1} 𝕜 (SeminormedRing.toPseudoMetricSpace.{u1} 𝕜 (SeminormedCommRing.toSeminormedRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) _inst_3 _inst_5 _inst_2 _inst_4 (LinearMap.flip.{u1, u1, u1, u1, u3, u2, u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) E F 𝕜 _inst_2 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))))) _inst_4 _inst_5 (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (instModuleToSemiringToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))) (MulActionWithZero.toMulAction.{u1, u1} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1)))) (CommMonoidWithZero.toZero.{u1} 𝕜 (CommSemiring.toCommMonoidWithZero.{u1} 𝕜 (CommRing.toCommSemiring.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 _inst_1))))) (MonoidWithZero.toMulActionWithZero.{u1} 𝕜 (Semiring.toMonoidWithZero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) (RingHom.id.{u1} 𝕜 (NonAssocRing.toNonAssocSemiring.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 _inst_1))))) B)) (LinearMap.polar.{u1, u3, u2} 𝕜 E F _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 B s)
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_weak_closed LinearMap.polar_weak_closedₓ'. -/
 /-- The polar set is closed in the weak topology induced by `B.flip`. -/
 theorem polar_weak_closed (s : Set E) : is_closed[WeakBilin.topologicalSpace B.flip] (B.polar s) :=
   by
@@ -146,6 +226,12 @@ variable [Module 𝕜 E] [Module 𝕜 F]
 
 variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)
 
+/- warning: linear_map.polar_univ -> LinearMap.polar_univ is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {E : Type.{u2}} {F : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u1} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u3} F] [_inst_4 : Module.{u1, u2} 𝕜 E (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_2] [_inst_5 : Module.{u1, u3} 𝕜 F (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3] (B : LinearMap.{u1, u1, u2, max u3 u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) E (LinearMap.{u1, u1, u3, u1} 𝕜 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) F 𝕜 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_2 (LinearMap.addCommMonoid.{u1, u1, u3, u1} 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))) _inst_4 (LinearMap.module.{u1, u1, u1, u3, u1} 𝕜 𝕜 𝕜 F 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) _inst_3 (AddCommGroup.toAddCommMonoid.{u1} 𝕜 (NormedAddCommGroup.toAddCommGroup.{u1} 𝕜 (NonUnitalNormedRing.toNormedAddCommGroup.{u1} 𝕜 (NormedRing.toNonUnitalNormedRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) _inst_5 (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Semiring.toModule.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))) (smulCommClass_self.{u1, u1} 𝕜 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))) (Monoid.toMulAction.{u1} 𝕜 (CommMonoid.toMonoid.{u1} 𝕜 (CommRing.toCommMonoid.{u1} 𝕜 (SeminormedCommRing.toCommRing.{u1} 𝕜 (NormedCommRing.toSeminormedCommRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))))))))), (LinearMap.SeparatingRight.{u1, u1, u1, u2, u3} 𝕜 𝕜 𝕜 E F (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_2 _inst_4 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 (NormedField.toField.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)))) _inst_3 _inst_5 (RingHom.id.{u1} 𝕜 (Semiring.toNonAssocSemiring.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (NormedRing.toRing.{u1} 𝕜 (NormedCommRing.toNormedRing.{u1} 𝕜 (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{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 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1))))))) B) -> (Eq.{succ u3} (Set.{u3} F) (LinearMap.polar.{u1, u2, u3} 𝕜 E F (NormedField.toNormedCommRing.{u1} 𝕜 (NontriviallyNormedField.toNormedField.{u1} 𝕜 _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 B (Set.univ.{u2} E)) (Singleton.singleton.{u3, u3} F (Set.{u3} F) (Set.hasSingleton.{u3} F) (OfNat.ofNat.{u3} F 0 (OfNat.mk.{u3} F 0 (Zero.zero.{u3} F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F _inst_3))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u3}} {E : Type.{u2}} {F : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u3} 𝕜] [_inst_2 : AddCommMonoid.{u2} E] [_inst_3 : AddCommMonoid.{u1} F] [_inst_4 : Module.{u3, u2} 𝕜 E (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_2] [_inst_5 : Module.{u3, u1} 𝕜 F (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3] (B : LinearMap.{u3, u3, u2, max u3 u1} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) E (LinearMap.{u3, u3, u1, u3} 𝕜 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) F 𝕜 _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRingToEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_2 (LinearMap.addCommMonoid.{u3, u3, u1, u3} 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRingToEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_4 (LinearMap.instModuleLinearMapAddCommMonoid.{u3, u3, u3, u1, u3} 𝕜 𝕜 𝕜 F 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) _inst_3 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u3} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))))) _inst_5 (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRingToEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (LinearMap.instModuleToSemiringToDivisionSemiringToSemifieldToAddCommMonoidToNonUnitalNonAssocSemiringToNonUnitalNonAssocRingToNonUnitalRingToNonUnitalCommRingToCommRingToEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))) (smulCommClass_self.{u3, u3} 𝕜 𝕜 (CommRing.toCommMonoid.{u3} 𝕜 (EuclideanDomain.toCommRing.{u3} 𝕜 (Field.toEuclideanDomain.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))) (MulActionWithZero.toMulAction.{u3, u3} 𝕜 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (CommMonoidWithZero.toZero.{u3} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u3} 𝕜 (Semifield.toCommGroupWithZero.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))))) (MonoidWithZero.toMulActionWithZero.{u3} 𝕜 (Semiring.toMonoidWithZero.{u3} 𝕜 (DivisionSemiring.toSemiring.{u3} 𝕜 (Semifield.toDivisionSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))))))), (LinearMap.SeparatingRight.{u3, u3, u3, u2, u1} 𝕜 𝕜 𝕜 E F (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_2 _inst_4 (Semifield.toCommSemiring.{u3} 𝕜 (Field.toSemifield.{u3} 𝕜 (NormedField.toField.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)))) _inst_3 _inst_5 (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) (RingHom.id.{u3} 𝕜 (NonAssocRing.toNonAssocSemiring.{u3} 𝕜 (Ring.toNonAssocRing.{u3} 𝕜 (NormedRing.toRing.{u3} 𝕜 (NormedCommRing.toNormedRing.{u3} 𝕜 (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1))))))) B) -> (Eq.{succ u1} (Set.{u1} F) (LinearMap.polar.{u3, u2, u1} 𝕜 E F (NormedField.toNormedCommRing.{u3} 𝕜 (NontriviallyNormedField.toNormedField.{u3} 𝕜 _inst_1)) _inst_2 _inst_3 _inst_4 _inst_5 B (Set.univ.{u2} E)) (Singleton.singleton.{u1, u1} F (Set.{u1} F) (Set.instSingletonSet.{u1} F) (OfNat.ofNat.{u1} F 0 (Zero.toOfNat0.{u1} F (AddMonoid.toZero.{u1} F (AddCommMonoid.toAddMonoid.{u1} F _inst_3))))))
+Case conversion may be inaccurate. Consider using '#align linear_map.polar_univ LinearMap.polar_univₓ'. -/
 theorem polar_univ (h : SeparatingRight B) : B.polar Set.univ = {(0 : F)} :=
   by
   rw [Set.eq_singleton_iff_unique_mem]

bcfa7268

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -156,7 +156,7 @@ theorem polar_univ (h : SeparatingRight B) : B.polar Set.univ = {(0 : F)} :=
     ‖B x y‖ = ‖c‖ * ‖B (c⁻¹ • x) y‖ := by
       rw [B.map_smul, LinearMap.smul_apply, Algebra.id.smul_eq_mul, norm_mul, norm_inv,
         mul_inv_cancel_left₀ hc.ne']
-    _ ≤ ε * 1 := mul_le_mul hcε.le (hy _ trivial) (norm_nonneg _) hε.le
+    _ ≤ ε * 1 := (mul_le_mul hcε.le (hy _ trivial) (norm_nonneg _) hε.le)
     _ = ε := mul_one _
     
 #align linear_map.polar_univ LinearMap.polar_univ

bcfa7268

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

bcfa7268

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

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

3556ded2

Diff

@@ -53,7 +53,7 @@ variable [Module 𝕜 E] [Module 𝕜 F]
 variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)
 
 /-- The (absolute) polar of `s : Set E` is given by the set of all `y : F` such that `‖B x y‖ ≤ 1`
-for all `x ∈ s`.-/
+for all `x ∈ s`. -/
 def polar (s : Set E) : Set F :=
   { y : F | ∀ x ∈ s, ‖B x y‖ ≤ 1 }
 #align linear_map.polar LinearMap.polar

bcfa7268

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

@@ -47,7 +47,6 @@ namespace LinearMap
 section NormedRing
 
 variable [NormedCommRing 𝕜] [AddCommMonoid E] [AddCommMonoid F]
-
 variable [Module 𝕜 E] [Module 𝕜 F]
 
 
@@ -134,7 +133,6 @@ end NormedRing
 section NontriviallyNormedField
 
 variable [NontriviallyNormedField 𝕜] [AddCommMonoid E] [AddCommMonoid F]
-
 variable [Module 𝕜 E] [Module 𝕜 F]

bcfa7268

chore: Move LinearMap.ker to a new file (#10233)

This shortens Mathlib.LinearAlgebra.Basic, which is both longer than we like and doesn't have a clear scope.

e50aeb4d

Diff

@@ -3,6 +3,7 @@ Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Kalle Kytölä
 -/
+import Mathlib.Algebra.EuclideanDomain.Instances
 import Mathlib.Analysis.Normed.Field.Basic
 import Mathlib.LinearAlgebra.SesquilinearForm
 import Mathlib.Topology.Algebra.Module.WeakDual

bcfa7268

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

@@ -37,7 +37,7 @@ polar
 -/
 
 
-variable {𝕜 E F : Type _}
+variable {𝕜 E F : Type*}
 
 open Topology

bcfa7268

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 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll, Kalle Kytölä
-
-! This file was ported from Lean 3 source module analysis.locally_convex.polar
-! leanprover-community/mathlib commit bcfa726826abd57587355b4b5b7e78ad6527b7e4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Normed.Field.Basic
 import Mathlib.LinearAlgebra.SesquilinearForm
 import Mathlib.Topology.Algebra.Module.WeakDual
 
+#align_import analysis.locally_convex.polar from "leanprover-community/mathlib"@"bcfa726826abd57587355b4b5b7e78ad6527b7e4"
+
 /-!
 # Polar set

bcfa7268

feat: golf using gcongr throughout the library (#4784)

Following on from #4702, another hundred sample uses of the gcongr tactic.

1507c181

Diff

@@ -151,7 +151,7 @@ theorem polar_univ (h : SeparatingRight B) : B.polar Set.univ = {(0 : F)} := by
     ‖B x y‖ = ‖c‖ * ‖B (c⁻¹ • x) y‖ := by
       rw [B.map_smul, LinearMap.smul_apply, Algebra.id.smul_eq_mul, norm_mul, norm_inv,
         mul_inv_cancel_left₀ hc.ne']
-    _ ≤ ε * 1 := (mul_le_mul hcε.le (hy _ trivial) (norm_nonneg _) hε.le)
+    _ ≤ ε * 1 := by gcongr; exact hy _ trivial
     _ = ε := mul_one _
 #align linear_map.polar_univ LinearMap.polar_univ

bcfa7268

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -55,7 +55,7 @@ variable [Module 𝕜 E] [Module 𝕜 F]
 
 variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)
 
-/-- The (absolute) polar of `s : set E` is given by the set of all `y : F` such that `‖B x y‖ ≤ 1`
+/-- The (absolute) polar of `s : Set E` is given by the set of all `y : F` such that `‖B x y‖ ≤ 1`
 for all `x ∈ s`.-/
 def polar (s : Set E) : Set F :=
   { y : F | ∀ x ∈ s, ‖B x y‖ ≤ 1 }
@@ -79,8 +79,8 @@ theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x
   simp only [polar_mem_iff, Set.mem_iInter, Set.mem_setOf_eq]
 #align linear_map.polar_eq_Inter LinearMap.polar_eq_iInter
 
-/-- The map `B.polar : set E → set F` forms an order-reversing Galois connection with
-`B.flip.polar : set F → set E`. We use `OrderDual.toDual` and `OrderDual.ofDual` to express
+/-- The map `B.polar : Set E → Set F` forms an order-reversing Galois connection with
+`B.flip.polar : Set F → Set E`. We use `OrderDual.toDual` and `OrderDual.ofDual` to express
 that `polar` is order-reversing. -/
 theorem polar_gc :
     GaloisConnection (OrderDual.toDual ∘ B.polar) (B.flip.polar ∘ OrderDual.ofDual) := fun _ _ =>

bcfa7268

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

Now that leanprover/lean4#2210 has been merged, this PR:

removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
removes many but not quite all set_option maxHeartbeats commands
makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

a6e1045f

Diff

@@ -52,7 +52,6 @@ variable [NormedCommRing 𝕜] [AddCommMonoid E] [AddCommMonoid F]
 
 variable [Module 𝕜 E] [Module 𝕜 F]
 
-set_option synthInstance.etaExperiment true -- Porting note: lean4#2074
 
 variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)
 
@@ -140,7 +139,6 @@ variable [NontriviallyNormedField 𝕜] [AddCommMonoid E] [AddCommMonoid F]
 
 variable [Module 𝕜 E] [Module 𝕜 F]
 
-set_option synthInstance.etaExperiment true -- Porting note: lean4#2074
 
 variable (B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜)

bcfa7268

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

supₛ → sSup
infₛ → sInf
supᵢ → iSup
infᵢ → iInf
bsupₛ → bsSup
binfₛ → bsInf
bsupᵢ → biSup
binfᵢ → biInf
csupₛ → csSup
cinfₛ → csInf
csupᵢ → ciSup
cinfᵢ → ciInf
unionₛ → sUnion
interₛ → sInter
unionᵢ → iUnion
interᵢ → iInter
bunionₛ → bsUnion
binterₛ → bsInter
bunionᵢ → biUnion
binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

d1eb6264

Diff

@@ -26,7 +26,7 @@ any bilinear form `B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜`, where `𝕜` is a no
 
 ## Main statements
 
-* `LinearMap.polar_eq_interᵢ`: The polar as an intersection.
+* `LinearMap.polar_eq_iInter`: The polar as an intersection.
 * `LinearMap.subset_bipolar`: The polar is a subset of the bipolar.
 * `LinearMap.polar_weak_closed`: The polar is closed in the weak topology induced by `B.flip`.
 
@@ -75,10 +75,10 @@ theorem zero_mem_polar (s : Set E) : (0 : F) ∈ B.polar s := fun _ _ => by
   simp only [map_zero, norm_zero, zero_le_one]
 #align linear_map.zero_mem_polar LinearMap.zero_mem_polar
 
-theorem polar_eq_interᵢ {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } := by
+theorem polar_eq_iInter {s : Set E} : B.polar s = ⋂ x ∈ s, { y : F | ‖B x y‖ ≤ 1 } := by
   ext
-  simp only [polar_mem_iff, Set.mem_interᵢ, Set.mem_setOf_eq]
-#align linear_map.polar_eq_Inter LinearMap.polar_eq_interᵢ
+  simp only [polar_mem_iff, Set.mem_iInter, Set.mem_setOf_eq]
+#align linear_map.polar_eq_Inter LinearMap.polar_eq_iInter
 
 /-- The map `B.polar : set E → set F` forms an order-reversing Galois connection with
 `B.flip.polar : set F → set E`. We use `OrderDual.toDual` and `OrderDual.ofDual` to express
@@ -89,9 +89,9 @@ theorem polar_gc :
 #align linear_map.polar_gc LinearMap.polar_gc
 
 @[simp]
-theorem polar_unionᵢ {ι} {s : ι → Set E} : B.polar (⋃ i, s i) = ⋂ i, B.polar (s i) :=
-  B.polar_gc.l_supᵢ
-#align linear_map.polar_Union LinearMap.polar_unionᵢ
+theorem polar_iUnion {ι} {s : ι → Set E} : B.polar (⋃ i, s i) = ⋂ i, B.polar (s i) :=
+  B.polar_gc.l_iSup
+#align linear_map.polar_Union LinearMap.polar_iUnion
 
 @[simp]
 theorem polar_union {s t : Set E} : B.polar (s ∪ t) = B.polar s ∩ B.polar t :=
@@ -127,8 +127,8 @@ theorem tripolar_eq_polar (s : Set E) : B.polar (B.flip.polar (B.polar s)) = B.p
 /-- The polar set is closed in the weak topology induced by `B.flip`. -/
 theorem polar_weak_closed (s : Set E) : IsClosed[WeakBilin.instTopologicalSpace B.flip]
     (B.polar s) := by
-  rw [polar_eq_interᵢ]
-  refine' isClosed_interᵢ fun x => isClosed_interᵢ fun _ => _
+  rw [polar_eq_iInter]
+  refine' isClosed_iInter fun x => isClosed_iInter fun _ => _
   exact isClosed_le (WeakBilin.eval_continuous B.flip x).norm continuous_const
 #align linear_map.polar_weak_closed LinearMap.polar_weak_closed

bcfa7268

chore: tidy various files (#3408)

7e7ba10b

Diff

@@ -22,7 +22,7 @@ any bilinear form `B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜`, where `𝕜` is a no
 
 ## Main definitions
 
-* `Linear_map.polar`: The polar of a bilinear form `B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜`.
+* `LinearMap.polar`: The polar of a bilinear form `B : E →ₗ[𝕜] F →ₗ[𝕜] 𝕜`.
 
 ## Main statements
 
@@ -155,7 +155,6 @@ theorem polar_univ (h : SeparatingRight B) : B.polar Set.univ = {(0 : F)} := by
         mul_inv_cancel_left₀ hc.ne']
     _ ≤ ε * 1 := (mul_le_mul hcε.le (hy _ trivial) (norm_nonneg _) hε.le)
     _ = ε := mul_one _
-
 #align linear_map.polar_univ LinearMap.polar_univ
 
 end NontriviallyNormedField

bcfa7268

feat: port Analysis.LocallyConvex.Polar (#3367)

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

5127295b

`analysis.locally_convex.polar` ⟷ `Mathlib.Analysis.LocallyConvex.Polar`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 10 + 604

analysis.locally_convex.polar ⟷ Mathlib.Analysis.LocallyConvex.Polar

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 10 + 604

`analysis.locally_convex.polar` ⟷ `Mathlib.Analysis.LocallyConvex.Polar`