analysis.normed_space.conformal_linear_map
⟷
Mathlib.Analysis.NormedSpace.ConformalLinearMap
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
-import Mathbin.Analysis.NormedSpace.Basic
-import Mathbin.Analysis.NormedSpace.LinearIsometry
+import Analysis.NormedSpace.Basic
+import Analysis.NormedSpace.LinearIsometry
#align_import analysis.normed_space.conformal_linear_map from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-
-! This file was ported from Lean 3 source module analysis.normed_space.conformal_linear_map
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.NormedSpace.Basic
import Mathbin.Analysis.NormedSpace.LinearIsometry
+#align_import analysis.normed_space.conformal_linear_map from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
/-!
# Conformal Linear Maps
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -64,32 +64,43 @@ variable {R M N G M' : Type _} [NormedField R] [SeminormedAddCommGroup M] [Semin
[SeminormedAddCommGroup G] [NormedSpace R M] [NormedSpace R N] [NormedSpace R G]
[NormedAddCommGroup M'] [NormedSpace R M'] {f : M →L[R] N} {g : N →L[R] G} {c : R}
+#print isConformalMap_id /-
theorem isConformalMap_id : IsConformalMap (id R M) :=
⟨1, one_ne_zero, id, by simp⟩
#align is_conformal_map_id isConformalMap_id
+-/
+#print IsConformalMap.smul /-
theorem IsConformalMap.smul (hf : IsConformalMap f) {c : R} (hc : c ≠ 0) : IsConformalMap (c • f) :=
by
rcases hf with ⟨c', hc', li, rfl⟩
exact ⟨c * c', mul_ne_zero hc hc', li, smul_smul _ _ _⟩
#align is_conformal_map.smul IsConformalMap.smul
+-/
+#print isConformalMap_const_smul /-
theorem isConformalMap_const_smul (hc : c ≠ 0) : IsConformalMap (c • id R M) :=
isConformalMap_id.smul hc
#align is_conformal_map_const_smul isConformalMap_const_smul
+-/
+#print LinearIsometry.isConformalMap /-
protected theorem LinearIsometry.isConformalMap (f' : M →ₗᵢ[R] N) :
IsConformalMap f'.toContinuousLinearMap :=
⟨1, one_ne_zero, f', (one_smul _ _).symm⟩
#align linear_isometry.is_conformal_map LinearIsometry.isConformalMap
+-/
+#print isConformalMap_of_subsingleton /-
@[nontriviality]
theorem isConformalMap_of_subsingleton [Subsingleton M] (f' : M →L[R] N) : IsConformalMap f' :=
⟨1, one_ne_zero, ⟨0, fun x => by simp [Subsingleton.elim x 0]⟩, Subsingleton.elim _ _⟩
#align is_conformal_map_of_subsingleton isConformalMap_of_subsingleton
+-/
namespace IsConformalMap
+#print IsConformalMap.comp /-
theorem comp (hg : IsConformalMap g) (hf : IsConformalMap f) : IsConformalMap (g.comp f) :=
by
rcases hf with ⟨cf, hcf, lif, rfl⟩
@@ -98,17 +109,22 @@ theorem comp (hg : IsConformalMap g) (hf : IsConformalMap f) : IsConformalMap (g
rw [smul_comp, comp_smul, mul_smul]
rfl
#align is_conformal_map.comp IsConformalMap.comp
+-/
+#print IsConformalMap.injective /-
protected theorem injective {f : M' →L[R] N} (h : IsConformalMap f) : Function.Injective f := by
rcases h with ⟨c, hc, li, rfl⟩; exact (smul_right_injective _ hc).comp li.injective
#align is_conformal_map.injective IsConformalMap.injective
+-/
+#print IsConformalMap.ne_zero /-
theorem ne_zero [Nontrivial M'] {f' : M' →L[R] N} (hf' : IsConformalMap f') : f' ≠ 0 :=
by
rintro rfl
rcases exists_ne (0 : M') with ⟨a, ha⟩
exact ha (hf'.injective rfl)
#align is_conformal_map.ne_zero IsConformalMap.ne_zero
+-/
end IsConformalMap
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -56,7 +56,7 @@ open Function LinearIsometry ContinuousLinearMap
a nonzero multiple of a linear isometry. -/
def IsConformalMap {R : Type _} {X Y : Type _} [NormedField R] [SeminormedAddCommGroup X]
[SeminormedAddCommGroup Y] [NormedSpace R X] [NormedSpace R Y] (f' : X →L[R] Y) :=
- ∃ (c : R)(hc : c ≠ 0)(li : X →ₗᵢ[R] Y), f' = c • li.toContinuousLinearMap
+ ∃ (c : R) (hc : c ≠ 0) (li : X →ₗᵢ[R] Y), f' = c • li.toContinuousLinearMap
#align is_conformal_map IsConformalMap
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -64,49 +64,25 @@ variable {R M N G M' : Type _} [NormedField R] [SeminormedAddCommGroup M] [Semin
[SeminormedAddCommGroup G] [NormedSpace R M] [NormedSpace R N] [NormedSpace R G]
[NormedAddCommGroup M'] [NormedSpace R M'] {f : M →L[R] N} {g : N →L[R] G} {c : R}
-/- warning: is_conformal_map_id -> isConformalMap_id is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2], IsConformalMap.{u1, u2, u2} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (ContinuousLinearMap.id.{u1, u2} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))
-but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : NormedField.{u2} R] [_inst_2 : SeminormedAddCommGroup.{u1} M] [_inst_5 : NormedSpace.{u2, u1} R M _inst_1 _inst_2], IsConformalMap.{u2, u1, u1} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (ContinuousLinearMap.id.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))
-Case conversion may be inaccurate. Consider using '#align is_conformal_map_id isConformalMap_idₓ'. -/
theorem isConformalMap_id : IsConformalMap (id R M) :=
⟨1, one_ne_zero, id, by simp⟩
#align is_conformal_map_id isConformalMap_id
-/- warning: is_conformal_map.smul -> IsConformalMap.smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_conformal_map.smul IsConformalMap.smulₓ'. -/
theorem IsConformalMap.smul (hf : IsConformalMap f) {c : R} (hc : c ≠ 0) : IsConformalMap (c • f) :=
by
rcases hf with ⟨c', hc', li, rfl⟩
exact ⟨c * c', mul_ne_zero hc hc', li, smul_smul _ _ _⟩
#align is_conformal_map.smul IsConformalMap.smul
-/- warning: is_conformal_map_const_smul -> isConformalMap_const_smul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_conformal_map_const_smul isConformalMap_const_smulₓ'. -/
theorem isConformalMap_const_smul (hc : c ≠ 0) : IsConformalMap (c • id R M) :=
isConformalMap_id.smul hc
#align is_conformal_map_const_smul isConformalMap_const_smul
-/- warning: linear_isometry.is_conformal_map -> LinearIsometry.isConformalMap is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] (f' : LinearIsometry.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M N _inst_2 _inst_3 (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (LinearIsometry.toContinuousLinearMap.{u1, u1, u2, u3} R R M N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) _inst_2 _inst_3 (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) f')
-but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : NormedField.{u3} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] (f' : LinearIsometry.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M N _inst_2 _inst_3 (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (LinearIsometry.toContinuousLinearMap.{u3, u3, u2, u1} R R M N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) _inst_2 _inst_3 (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) f')
-Case conversion may be inaccurate. Consider using '#align linear_isometry.is_conformal_map LinearIsometry.isConformalMapₓ'. -/
protected theorem LinearIsometry.isConformalMap (f' : M →ₗᵢ[R] N) :
IsConformalMap f'.toContinuousLinearMap :=
⟨1, one_ne_zero, f', (one_smul _ _).symm⟩
#align linear_isometry.is_conformal_map LinearIsometry.isConformalMap
-/- warning: is_conformal_map_of_subsingleton -> isConformalMap_of_subsingleton is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] [_inst_10 : Subsingleton.{succ u2} M] (f' : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f'
-but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : NormedField.{u2} R] [_inst_2 : SeminormedAddCommGroup.{u3} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u2, u1} R N _inst_1 _inst_3] [_inst_10 : Subsingleton.{succ u3} M] (f' : ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u3} M (PseudoMetricSpace.toUniformSpace.{u3} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} M (SeminormedAddCommGroup.toAddCommGroup.{u3} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u2, u3, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f'
-Case conversion may be inaccurate. Consider using '#align is_conformal_map_of_subsingleton isConformalMap_of_subsingletonₓ'. -/
@[nontriviality]
theorem isConformalMap_of_subsingleton [Subsingleton M] (f' : M →L[R] N) : IsConformalMap f' :=
⟨1, one_ne_zero, ⟨0, fun x => by simp [Subsingleton.elim x 0]⟩, Subsingleton.elim _ _⟩
@@ -114,9 +90,6 @@ theorem isConformalMap_of_subsingleton [Subsingleton M] (f' : M →L[R] N) : IsC
namespace IsConformalMap
-/- warning: is_conformal_map.comp -> IsConformalMap.comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_conformal_map.comp IsConformalMap.compₓ'. -/
theorem comp (hg : IsConformalMap g) (hf : IsConformalMap f) : IsConformalMap (g.comp f) :=
by
rcases hf with ⟨cf, hcf, lif, rfl⟩
@@ -126,16 +99,10 @@ theorem comp (hg : IsConformalMap g) (hf : IsConformalMap f) : IsConformalMap (g
rfl
#align is_conformal_map.comp IsConformalMap.comp
-/- warning: is_conformal_map.injective -> IsConformalMap.injective is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_conformal_map.injective IsConformalMap.injectiveₓ'. -/
protected theorem injective {f : M' →L[R] N} (h : IsConformalMap f) : Function.Injective f := by
rcases h with ⟨c, hc, li, rfl⟩; exact (smul_right_injective _ hc).comp li.injective
#align is_conformal_map.injective IsConformalMap.injective
-/- warning: is_conformal_map.ne_zero -> IsConformalMap.ne_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_conformal_map.ne_zero IsConformalMap.ne_zeroₓ'. -/
theorem ne_zero [Nontrivial M'] {f' : M' →L[R] N} (hf' : IsConformalMap f') : f' ≠ 0 :=
by
rintro rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -129,10 +129,8 @@ theorem comp (hg : IsConformalMap g) (hf : IsConformalMap f) : IsConformalMap (g
/- warning: is_conformal_map.injective -> IsConformalMap.injective is a dubious translation:
<too large>
Case conversion may be inaccurate. Consider using '#align is_conformal_map.injective IsConformalMap.injectiveₓ'. -/
-protected theorem injective {f : M' →L[R] N} (h : IsConformalMap f) : Function.Injective f :=
- by
- rcases h with ⟨c, hc, li, rfl⟩
- exact (smul_right_injective _ hc).comp li.injective
+protected theorem injective {f : M' →L[R] N} (h : IsConformalMap f) : Function.Injective f := by
+ rcases h with ⟨c, hc, li, rfl⟩; exact (smul_right_injective _ hc).comp li.injective
#align is_conformal_map.injective IsConformalMap.injective
/- warning: is_conformal_map.ne_zero -> IsConformalMap.ne_zero is a dubious translation:
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -75,10 +75,7 @@ theorem isConformalMap_id : IsConformalMap (id R M) :=
#align is_conformal_map_id isConformalMap_id
/- warning: is_conformal_map.smul -> IsConformalMap.smul is a dubious translation:
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(SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (forall {c : R}, (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))))))) -> (IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 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(NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R 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(Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} 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(PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3)))))) (Module.toMulActionWithZero.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3))) (ContinuousLinearMap.module.{u1, u1, u1, u2, u3} R R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (smulCommClass_self.{u1, u3} R N (CommRing.toCommMonoid.{u1} R (SeminormedCommRing.toCommRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R 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(NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (Module.toMulActionWithZero.{u1, u3} R N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6))))) (BoundedSMul.continuousSMul.{u1, u3} R N (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (Module.toMulActionWithZero.{u1, u3} R N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6))))) (NormedSpace.boundedSMul.{u1, u3} R N _inst_1 _inst_3 _inst_6))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3))))))) c f)))
-but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : NormedField.{u3} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] {f : ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (forall {c : R}, (Ne.{succ u3} R c (OfNat.ofNat.{u3} R 0 (Zero.toOfNat0.{u3} R (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))))) -> (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R 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(ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) 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(UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (SMulWithZero.toSMulZeroClass.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (MulActionWithZero.toSMulWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Module.toMulActionWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} N _inst_3))) (ContinuousLinearMap.module.{u3, u3, u3, u2, u1} R R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (smulCommClass_self.{u3, u1} R N (CommRing.toCommMonoid.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (NormedField.toField.{u3} R _inst_1)))) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)))) (ContinuousSMul.continuousConstSMul.{u3, u1} R N (UniformSpace.toTopologicalSpace.{u3} R (PseudoMetricSpace.toUniformSpace.{u3} R (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (BoundedSMul.continuousSMul.{u3, u1} R N (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (NormedSpace.boundedSMul.{u3, u1} R N _inst_1 _inst_3 _inst_6))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} N _inst_3)))))))) c f)))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_conformal_map.smul IsConformalMap.smulₓ'. -/
theorem IsConformalMap.smul (hf : IsConformalMap f) {c : R} (hc : c ≠ 0) : IsConformalMap (c • f) :=
by
@@ -87,10 +84,7 @@ theorem IsConformalMap.smul (hf : IsConformalMap f) {c : R} (hc : c ≠ 0) : IsC
#align is_conformal_map.smul IsConformalMap.smul
/- warning: is_conformal_map_const_smul -> isConformalMap_const_smul is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] {c : R}, (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))))))) -> (IsConformalMap.{u1, u2, u2} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (SMul.smul.{u1, u2} R (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (SMulZeroClass.toHasSmul.{u1, u2} R (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddZeroClass.toHasZero.{u2} (ContinuousLinearMap.{u1, u1, u2, 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(AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddMonoid.toAddZeroClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M 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(NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddCommMonoid.toAddMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R 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(AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} M _inst_2))))))) c (ContinuousLinearMap.id.{u1, u2} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))))
-but is expected to have type
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(RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (instHSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Algebra.toSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))) (ContinuousLinearMap.semiring.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_2)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} M _inst_2))) (ContinuousLinearMap.algebra.{u2, u1} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} M _inst_2) (ContinuousSMul.continuousConstSMul.{u2, u1} R M (UniformSpace.toTopologicalSpace.{u2} R (PseudoMetricSpace.toUniformSpace.{u2} R (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (BoundedSMul.continuousSMul.{u2, u1} R M (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2) (CommMonoidWithZero.toZero.{u2} R (CommGroupWithZero.toCommMonoidWithZero.{u2} R (Semifield.toCommGroupWithZero.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (NormedSpace.boundedSMul.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))) c (ContinuousLinearMap.id.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_conformal_map_const_smul isConformalMap_const_smulₓ'. -/
theorem isConformalMap_const_smul (hc : c ≠ 0) : IsConformalMap (c • id R M) :=
isConformalMap_id.smul hc
@@ -121,10 +115,7 @@ theorem isConformalMap_of_subsingleton [Subsingleton M] (f' : M →L[R] N) : IsC
namespace IsConformalMap
/- warning: is_conformal_map.comp -> IsConformalMap.comp is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {G : Type.{u4}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_4 : SeminormedAddCommGroup.{u4} G] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] [_inst_7 : NormedSpace.{u1, u4} R G _inst_1 _inst_4] {f : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)} {g : ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u4} G (PseudoMetricSpace.toUniformSpace.{u4} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u4} G (SeminormedAddCommGroup.toAddCommGroup.{u4} G _inst_4)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u1, u4} R G _inst_1 _inst_4 _inst_7)}, (IsConformalMap.{u1, u3, u4} R N G _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g) -> (IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (IsConformalMap.{u1, u2, u4} R M G _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u4} G (PseudoMetricSpace.toUniformSpace.{u4} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u4} G (SeminormedAddCommGroup.toAddCommGroup.{u4} G _inst_4)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u1, u4} R G _inst_1 _inst_4 _inst_7) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))))) g f))
-but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u1}} {N : Type.{u3}} {G : Type.{u2}} [_inst_1 : NormedField.{u4} R] [_inst_2 : SeminormedAddCommGroup.{u1} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_4 : SeminormedAddCommGroup.{u2} G] [_inst_5 : NormedSpace.{u4, u1} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u4, u3} R N _inst_1 _inst_3] [_inst_7 : NormedSpace.{u4, u2} R G _inst_1 _inst_4] {f : ContinuousLinearMap.{u4, u4, u1, u3} R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u4, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u4, u3} R N _inst_1 _inst_3 _inst_6)} {g : ContinuousLinearMap.{u4, u4, u3, u2} R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))))) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} G (SeminormedAddCommGroup.toAddCommGroup.{u2} G _inst_4)) (NormedSpace.toModule.{u4, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u4, u2} R G _inst_1 _inst_4 _inst_7)}, (IsConformalMap.{u4, u3, u2} R N G _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g) -> (IsConformalMap.{u4, u1, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (IsConformalMap.{u4, u1, u2} R M G _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (ContinuousLinearMap.comp.{u4, u4, u4, u1, u3, u2} R R R (DivisionSemiring.toSemiring.{u4} R 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+<too large>
Case conversion may be inaccurate. Consider using '#align is_conformal_map.comp IsConformalMap.compₓ'. -/
theorem comp (hg : IsConformalMap g) (hf : IsConformalMap f) : IsConformalMap (g.comp f) :=
by
@@ -136,10 +127,7 @@ theorem comp (hg : IsConformalMap g) (hf : IsConformalMap f) : IsConformalMap (g
#align is_conformal_map.comp IsConformalMap.comp
/- warning: is_conformal_map.injective -> IsConformalMap.injective is a dubious translation:
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(SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)))) f))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_conformal_map.injective IsConformalMap.injectiveₓ'. -/
protected theorem injective {f : M' →L[R] N} (h : IsConformalMap f) : Function.Injective f :=
by
@@ -148,10 +136,7 @@ protected theorem injective {f : M' →L[R] N} (h : IsConformalMap f) : Function
#align is_conformal_map.injective IsConformalMap.injective
/- warning: is_conformal_map.ne_zero -> IsConformalMap.ne_zero is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} {N : Type.{u2}} {M' : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_3 : SeminormedAddCommGroup.{u2} N] [_inst_6 : NormedSpace.{u1, u2} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u3} M'] [_inst_9 : NormedSpace.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)] [_inst_10 : Nontrivial.{u3} M'] {f' : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' 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(AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) 0 (Zero.zero.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6))))))
-but is expected to have type
- forall {R : Type.{u2}} {N : Type.{u1}} {M' : Type.{u3}} [_inst_1 : NormedField.{u2} R] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_6 : NormedSpace.{u2, u1} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u3} M'] [_inst_9 : NormedSpace.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)] [_inst_10 : Nontrivial.{u3} M'] {f' : ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u2, u3, u1} R M' N _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_3 _inst_9 _inst_6 f') -> (Ne.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) f' (OfNat.ofNat.{max u1 u3} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) 0 (Zero.toOfNat0.{max u1 u3} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)))))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_conformal_map.ne_zero IsConformalMap.ne_zeroₓ'. -/
theorem ne_zero [Nontrivial M'] {f' : M' →L[R] N} (hf' : IsConformalMap f') : f' ≠ 0 :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -78,7 +78,7 @@ theorem isConformalMap_id : IsConformalMap (id R M) :=
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] {f : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (forall {c : R}, (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))))))) -> (IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (SMul.smul.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (SMulZeroClass.toHasSmul.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3)))))) (Module.toMulActionWithZero.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3))) (ContinuousLinearMap.module.{u1, u1, u1, u2, u3} R R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (smulCommClass_self.{u1, u3} R N (CommRing.toCommMonoid.{u1} R (SeminormedCommRing.toCommRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (Module.toMulActionWithZero.{u1, u3} R N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)))) (ContinuousSMul.continuousConstSMul.{u1, u3} R N (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (SMulZeroClass.toHasSmul.{u1, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (Module.toMulActionWithZero.{u1, u3} R N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6))))) (BoundedSMul.continuousSMul.{u1, u3} R N (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (Module.toMulActionWithZero.{u1, u3} R N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6))))) (NormedSpace.boundedSMul.{u1, u3} R N _inst_1 _inst_3 _inst_6))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3))))))) c f)))
but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : NormedField.{u3} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] {f : ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (forall {c : R}, (Ne.{succ u3} R c (OfNat.ofNat.{u3} R 0 (Zero.toOfNat0.{u3} R (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))))) -> (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (instHSMul.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (SMulZeroClass.toSMul.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (SMulWithZero.toSMulZeroClass.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (MulActionWithZero.toSMulWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Module.toMulActionWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} N _inst_3))) (ContinuousLinearMap.module.{u3, u3, u3, u2, u1} R R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (smulCommClass_self.{u3, u1} R N (CommRing.toCommMonoid.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (NormedField.toField.{u3} R _inst_1)))) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)))) (ContinuousSMul.continuousConstSMul.{u3, u1} R N (UniformSpace.toTopologicalSpace.{u3} R (PseudoMetricSpace.toUniformSpace.{u3} R (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (BoundedSMul.continuousSMul.{u3, u1} R N (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (NormedSpace.boundedSMul.{u3, u1} R N _inst_1 _inst_3 _inst_6))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} N _inst_3)))))))) c f)))
+ forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : NormedField.{u3} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] {f : ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (forall {c : R}, (Ne.{succ u3} R c (OfNat.ofNat.{u3} R 0 (Zero.toOfNat0.{u3} R (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))))) -> (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (instHSMul.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (SMulZeroClass.toSMul.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (SMulWithZero.toSMulZeroClass.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (MulActionWithZero.toSMulWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Module.toMulActionWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} N _inst_3))) (ContinuousLinearMap.module.{u3, u3, u3, u2, u1} R R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (smulCommClass_self.{u3, u1} R N (CommRing.toCommMonoid.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (NormedField.toField.{u3} R _inst_1)))) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)))) (ContinuousSMul.continuousConstSMul.{u3, u1} R N (UniformSpace.toTopologicalSpace.{u3} R (PseudoMetricSpace.toUniformSpace.{u3} R (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (BoundedSMul.continuousSMul.{u3, u1} R N (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (NormedSpace.boundedSMul.{u3, u1} R N _inst_1 _inst_3 _inst_6))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} N _inst_3)))))))) c f)))
Case conversion may be inaccurate. Consider using '#align is_conformal_map.smul IsConformalMap.smulₓ'. -/
theorem IsConformalMap.smul (hf : IsConformalMap f) {c : R} (hc : c ≠ 0) : IsConformalMap (c • f) :=
by
@@ -90,7 +90,7 @@ theorem IsConformalMap.smul (hf : IsConformalMap f) {c : R} (hc : c ≠ 0) : IsC
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] {c : R}, (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))))))) -> (IsConformalMap.{u1, u2, u2} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (SMul.smul.{u1, u2} R (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (SMulZeroClass.toHasSmul.{u1, u2} R (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddZeroClass.toHasZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddMonoid.toAddZeroClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddCommMonoid.toAddMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M 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(AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddMonoid.toAddZeroClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M 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(NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (LipschitzAdd.continuousAdd.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} M _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (LipschitzAdd.continuousAdd.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} M _inst_2))) (ContinuousLinearMap.module.{u1, u1, u1, u2, u2} R R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (smulCommClass_self.{u1, u2} R M (CommRing.toCommMonoid.{u1} R (SeminormedCommRing.toCommRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)))) (ContinuousSMul.continuousConstSMul.{u1, u2} R M (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))))) (BoundedSMul.continuousSMul.{u1, u2} R M (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))))) (NormedSpace.boundedSMul.{u1, u2} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (LipschitzAdd.continuousAdd.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} M _inst_2))))))) c (ContinuousLinearMap.id.{u1, u2} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : NormedField.{u2} R] [_inst_2 : SeminormedAddCommGroup.{u1} M] [_inst_5 : NormedSpace.{u2, u1} R M _inst_1 _inst_2] {c : R}, (Ne.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommGroupWithZero.toCommMonoidWithZero.{u2} R (Semifield.toCommGroupWithZero.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))))) -> (IsConformalMap.{u2, u1, u1} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (HSMul.hSMul.{u2, u1, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (instHSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Algebra.toSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))) (ContinuousLinearMap.semiring.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_2)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_2))) (ContinuousLinearMap.algebra.{u2, u1} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_2) (ContinuousSMul.continuousConstSMul.{u2, u1} R M (UniformSpace.toTopologicalSpace.{u2} R (PseudoMetricSpace.toUniformSpace.{u2} R (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (BoundedSMul.continuousSMul.{u2, u1} R M (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2) (CommMonoidWithZero.toZero.{u2} R (CommGroupWithZero.toCommMonoidWithZero.{u2} R (Semifield.toCommGroupWithZero.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (NormedSpace.boundedSMul.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))) c (ContinuousLinearMap.id.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : NormedField.{u2} R] [_inst_2 : SeminormedAddCommGroup.{u1} M] [_inst_5 : NormedSpace.{u2, u1} R M _inst_1 _inst_2] {c : R}, (Ne.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommGroupWithZero.toCommMonoidWithZero.{u2} R (Semifield.toCommGroupWithZero.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))))) -> (IsConformalMap.{u2, u1, u1} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (HSMul.hSMul.{u2, u1, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (instHSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Algebra.toSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))) (ContinuousLinearMap.semiring.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_2)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} M _inst_2))) (ContinuousLinearMap.algebra.{u2, u1} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} M _inst_2) (ContinuousSMul.continuousConstSMul.{u2, u1} R M (UniformSpace.toTopologicalSpace.{u2} R (PseudoMetricSpace.toUniformSpace.{u2} R (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (BoundedSMul.continuousSMul.{u2, u1} R M (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2) (CommMonoidWithZero.toZero.{u2} R (CommGroupWithZero.toCommMonoidWithZero.{u2} R (Semifield.toCommGroupWithZero.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (NormedSpace.boundedSMul.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))) c (ContinuousLinearMap.id.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))
Case conversion may be inaccurate. Consider using '#align is_conformal_map_const_smul isConformalMap_const_smulₓ'. -/
theorem isConformalMap_const_smul (hc : c ≠ 0) : IsConformalMap (c • id R M) :=
isConformalMap_id.smul hc
mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1
@@ -78,7 +78,7 @@ theorem isConformalMap_id : IsConformalMap (id R M) :=
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] {f : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (forall {c : R}, (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))))))) -> (IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (SMul.smul.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (SMulZeroClass.toHasSmul.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3)))))) (SMulWithZero.toSmulZeroClass.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3)))))) (MulActionWithZero.toSMulWithZero.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3)))))) (Module.toMulActionWithZero.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3))) (ContinuousLinearMap.module.{u1, u1, u1, u2, u3} R R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (smulCommClass_self.{u1, u3} R N (CommRing.toCommMonoid.{u1} R (SeminormedCommRing.toCommRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (Module.toMulActionWithZero.{u1, u3} R N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)))) (ContinuousSMul.continuousConstSMul.{u1, u3} R N (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (SMulZeroClass.toHasSmul.{u1, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (Module.toMulActionWithZero.{u1, u3} R N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6))))) (BoundedSMul.continuousSMul.{u1, u3} R N (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (Module.toMulActionWithZero.{u1, u3} R N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6))))) (NormedSpace.boundedSMul.{u1, u3} R N _inst_1 _inst_3 _inst_6))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3))))))) c f)))
but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : NormedField.{u3} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] {f : ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (forall {c : R}, (Ne.{succ u3} R c (OfNat.ofNat.{u3} R 0 (Zero.toOfNat0.{u3} R (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))))) -> (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (instHSMul.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (SMulZeroClass.toSMul.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (SMulWithZero.toSMulZeroClass.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (MulActionWithZero.toSMulWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Module.toMulActionWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} N _inst_3))) (ContinuousLinearMap.module.{u3, u3, u3, u2, u1} R R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (smulCommClass_self.{u3, u1} R N (CommRing.toCommMonoid.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (NormedField.toField.{u3} R _inst_1)))) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)))) (ContinuousSMul.continuousConstSMul.{u3, u1} R N (UniformSpace.toTopologicalSpace.{u3} R (PseudoMetricSpace.toUniformSpace.{u3} R (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (BoundedSMul.continuousSMul.{u3, u1} R N (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (NormedSpace.boundedSMul.{u3, u1} R N _inst_1 _inst_3 _inst_6))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} N _inst_3)))))))) c f)))
+ forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : NormedField.{u3} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] {f : ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (forall {c : R}, (Ne.{succ u3} R c (OfNat.ofNat.{u3} R 0 (Zero.toOfNat0.{u3} R (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))))) -> (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (instHSMul.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (SMulZeroClass.toSMul.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (SMulWithZero.toSMulZeroClass.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (MulActionWithZero.toSMulWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Module.toMulActionWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} N _inst_3))) (ContinuousLinearMap.module.{u3, u3, u3, u2, u1} R R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (smulCommClass_self.{u3, u1} R N (CommRing.toCommMonoid.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (NormedField.toField.{u3} R _inst_1)))) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)))) (ContinuousSMul.continuousConstSMul.{u3, u1} R N (UniformSpace.toTopologicalSpace.{u3} R (PseudoMetricSpace.toUniformSpace.{u3} R (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (BoundedSMul.continuousSMul.{u3, u1} R N (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (NormedSpace.boundedSMul.{u3, u1} R N _inst_1 _inst_3 _inst_6))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} N _inst_3)))))))) c f)))
Case conversion may be inaccurate. Consider using '#align is_conformal_map.smul IsConformalMap.smulₓ'. -/
theorem IsConformalMap.smul (hf : IsConformalMap f) {c : R} (hc : c ≠ 0) : IsConformalMap (c • f) :=
by
@@ -90,7 +90,7 @@ theorem IsConformalMap.smul (hf : IsConformalMap f) {c : R} (hc : c ≠ 0) : IsC
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] {c : R}, (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))))))) -> (IsConformalMap.{u1, u2, u2} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (SMul.smul.{u1, u2} R (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (SMulZeroClass.toHasSmul.{u1, u2} R (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddZeroClass.toHasZero.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddMonoid.toAddZeroClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddCommMonoid.toAddMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M 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(AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddMonoid.toAddZeroClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M 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(NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (LipschitzAdd.continuousAdd.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} M _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (LipschitzAdd.continuousAdd.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} M _inst_2))) (ContinuousLinearMap.module.{u1, u1, u1, u2, u2} R R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (smulCommClass_self.{u1, u2} R M (CommRing.toCommMonoid.{u1} R (SeminormedCommRing.toCommRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)))) (ContinuousSMul.continuousConstSMul.{u1, u2} R M (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))))) (BoundedSMul.continuousSMul.{u1, u2} R M (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))))) (NormedSpace.boundedSMul.{u1, u2} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (LipschitzAdd.continuousAdd.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} M _inst_2))))))) c (ContinuousLinearMap.id.{u1, u2} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))))
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : NormedField.{u2} R] [_inst_2 : SeminormedAddCommGroup.{u1} M] [_inst_5 : NormedSpace.{u2, u1} R M _inst_1 _inst_2] {c : R}, (Ne.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommGroupWithZero.toCommMonoidWithZero.{u2} R (Semifield.toCommGroupWithZero.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))))) -> (IsConformalMap.{u2, u1, u1} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (HSMul.hSMul.{u2, u1, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (instHSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Algebra.toSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))) (ContinuousLinearMap.semiring.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_2)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_2))) (ContinuousLinearMap.algebra.{u2, u1} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_2) (ContinuousSMul.continuousConstSMul.{u2, u1} R M (UniformSpace.toTopologicalSpace.{u2} R (PseudoMetricSpace.toUniformSpace.{u2} R (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (BoundedSMul.continuousSMul.{u2, u1} R M (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2) (CommMonoidWithZero.toZero.{u2} R (CommGroupWithZero.toCommMonoidWithZero.{u2} R (Semifield.toCommGroupWithZero.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (NormedSpace.boundedSMul.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))) c (ContinuousLinearMap.id.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : NormedField.{u2} R] [_inst_2 : SeminormedAddCommGroup.{u1} M] [_inst_5 : NormedSpace.{u2, u1} R M _inst_1 _inst_2] {c : R}, (Ne.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommGroupWithZero.toCommMonoidWithZero.{u2} R (Semifield.toCommGroupWithZero.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))))) -> (IsConformalMap.{u2, u1, u1} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (HSMul.hSMul.{u2, u1, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (instHSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Algebra.toSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))) (ContinuousLinearMap.semiring.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_2)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_2))) (ContinuousLinearMap.algebra.{u2, u1} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_2) (ContinuousSMul.continuousConstSMul.{u2, u1} R M (UniformSpace.toTopologicalSpace.{u2} R (PseudoMetricSpace.toUniformSpace.{u2} R (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (BoundedSMul.continuousSMul.{u2, u1} R M (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2) (CommMonoidWithZero.toZero.{u2} R (CommGroupWithZero.toCommMonoidWithZero.{u2} R (Semifield.toCommGroupWithZero.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (NormedSpace.boundedSMul.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))) c (ContinuousLinearMap.id.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))
Case conversion may be inaccurate. Consider using '#align is_conformal_map_const_smul isConformalMap_const_smulₓ'. -/
theorem isConformalMap_const_smul (hc : c ≠ 0) : IsConformalMap (c • id R M) :=
isConformalMap_id.smul hc
@@ -100,7 +100,7 @@ theorem isConformalMap_const_smul (hc : c ≠ 0) : IsConformalMap (c • id R M)
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] (f' : LinearIsometry.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M N _inst_2 _inst_3 (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (LinearIsometry.toContinuousLinearMap.{u1, u1, u2, u3} R R M N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) _inst_2 _inst_3 (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) f')
but is expected to have type
- forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : NormedField.{u3} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] (f' : LinearIsometry.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M N _inst_2 _inst_3 (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (LinearIsometry.toContinuousLinearMap.{u3, u3, u2, u1} R R M N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) _inst_2 _inst_3 (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) f')
+ forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : NormedField.{u3} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] (f' : LinearIsometry.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M N _inst_2 _inst_3 (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (LinearIsometry.toContinuousLinearMap.{u3, u3, u2, u1} R R M N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) _inst_2 _inst_3 (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) f')
Case conversion may be inaccurate. Consider using '#align linear_isometry.is_conformal_map LinearIsometry.isConformalMapₓ'. -/
protected theorem LinearIsometry.isConformalMap (f' : M →ₗᵢ[R] N) :
IsConformalMap f'.toContinuousLinearMap :=
@@ -111,7 +111,7 @@ protected theorem LinearIsometry.isConformalMap (f' : M →ₗᵢ[R] N) :
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] [_inst_10 : Subsingleton.{succ u2} M] (f' : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f'
but is expected to have type
- forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : NormedField.{u2} R] [_inst_2 : SeminormedAddCommGroup.{u3} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u2, u1} R N _inst_1 _inst_3] [_inst_10 : Subsingleton.{succ u3} M] (f' : ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u3} M (PseudoMetricSpace.toUniformSpace.{u3} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} M (SeminormedAddCommGroup.toAddCommGroup.{u3} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u2, u3, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f'
+ forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : NormedField.{u2} R] [_inst_2 : SeminormedAddCommGroup.{u3} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u2, u1} R N _inst_1 _inst_3] [_inst_10 : Subsingleton.{succ u3} M] (f' : ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u3} M (PseudoMetricSpace.toUniformSpace.{u3} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} M (SeminormedAddCommGroup.toAddCommGroup.{u3} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u2, u3, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f'
Case conversion may be inaccurate. Consider using '#align is_conformal_map_of_subsingleton isConformalMap_of_subsingletonₓ'. -/
@[nontriviality]
theorem isConformalMap_of_subsingleton [Subsingleton M] (f' : M →L[R] N) : IsConformalMap f' :=
@@ -124,7 +124,7 @@ namespace IsConformalMap
lean 3 declaration is
forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {G : Type.{u4}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_4 : SeminormedAddCommGroup.{u4} G] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] [_inst_7 : NormedSpace.{u1, u4} R G _inst_1 _inst_4] {f : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)} {g : ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u4} G (PseudoMetricSpace.toUniformSpace.{u4} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u4} G (SeminormedAddCommGroup.toAddCommGroup.{u4} G _inst_4)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u1, u4} R G _inst_1 _inst_4 _inst_7)}, (IsConformalMap.{u1, u3, u4} R N G _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g) -> (IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (IsConformalMap.{u1, u2, u4} R M G _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u4} G (PseudoMetricSpace.toUniformSpace.{u4} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u4} G (SeminormedAddCommGroup.toAddCommGroup.{u4} G _inst_4)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u1, u4} R G _inst_1 _inst_4 _inst_7) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))))) g f))
but is expected to have type
- forall {R : Type.{u4}} {M : Type.{u1}} {N : Type.{u3}} {G : Type.{u2}} [_inst_1 : NormedField.{u4} R] [_inst_2 : SeminormedAddCommGroup.{u1} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_4 : SeminormedAddCommGroup.{u2} G] [_inst_5 : NormedSpace.{u4, u1} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u4, u3} R N _inst_1 _inst_3] [_inst_7 : NormedSpace.{u4, u2} R G _inst_1 _inst_4] {f : ContinuousLinearMap.{u4, u4, u1, u3} R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u4, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u4, u3} R N _inst_1 _inst_3 _inst_6)} {g : ContinuousLinearMap.{u4, u4, u3, u2} R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1)))))) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} G (SeminormedAddCommGroup.toAddCommGroup.{u2} G _inst_4)) (NormedSpace.toModule.{u4, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u4, u2} R G _inst_1 _inst_4 _inst_7)}, (IsConformalMap.{u4, u3, u2} R N G _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g) -> (IsConformalMap.{u4, u1, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (IsConformalMap.{u4, u1, u2} R M G _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (ContinuousLinearMap.comp.{u4, u4, u4, u1, u3, u2} R R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1)))))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1)))))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} G (SeminormedAddCommGroup.toAddCommGroup.{u2} G _inst_4)) (NormedSpace.toModule.{u4, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u4, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u4, u2} R G _inst_1 _inst_4 _inst_7) (RingHomCompTriple.ids.{u4, u4} R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1))))))) g f))
+ forall {R : Type.{u4}} {M : Type.{u1}} {N : Type.{u3}} {G : Type.{u2}} [_inst_1 : NormedField.{u4} R] [_inst_2 : SeminormedAddCommGroup.{u1} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_4 : SeminormedAddCommGroup.{u2} G] [_inst_5 : NormedSpace.{u4, u1} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u4, u3} R N _inst_1 _inst_3] [_inst_7 : NormedSpace.{u4, u2} R G _inst_1 _inst_4] {f : ContinuousLinearMap.{u4, u4, u1, u3} R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u4, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u4, u3} R N _inst_1 _inst_3 _inst_6)} {g : ContinuousLinearMap.{u4, u4, u3, u2} R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))))) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} G (SeminormedAddCommGroup.toAddCommGroup.{u2} G _inst_4)) (NormedSpace.toModule.{u4, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u4, u2} R G _inst_1 _inst_4 _inst_7)}, (IsConformalMap.{u4, u3, u2} R N G _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g) -> (IsConformalMap.{u4, u1, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (IsConformalMap.{u4, u1, u2} R M G _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (ContinuousLinearMap.comp.{u4, u4, u4, u1, u3, u2} R R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} G (SeminormedAddCommGroup.toAddCommGroup.{u2} G _inst_4)) (NormedSpace.toModule.{u4, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u4, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u4, u2} R G _inst_1 _inst_4 _inst_7) (RingHomCompTriple.ids.{u4, u4} R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (Semiring.toNonAssocSemiring.{u4} R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1))))))) g f))
Case conversion may be inaccurate. Consider using '#align is_conformal_map.comp IsConformalMap.compₓ'. -/
theorem comp (hg : IsConformalMap g) (hf : IsConformalMap f) : IsConformalMap (g.comp f) :=
by
@@ -139,7 +139,7 @@ theorem comp (hg : IsConformalMap g) (hf : IsConformalMap f) : IsConformalMap (g
lean 3 declaration is
forall {R : Type.{u1}} {N : Type.{u2}} {M' : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_3 : SeminormedAddCommGroup.{u2} N] [_inst_6 : NormedSpace.{u1, u2} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u3} M'] [_inst_9 : NormedSpace.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)] {f : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u1, u3, u2} R M' N _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_3 _inst_9 _inst_6 f) -> (Function.Injective.{succ u3, succ u2} M' N (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) (fun (_x : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) => M' -> N) (ContinuousLinearMap.toFun.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) f))
but is expected to have type
- forall {R : Type.{u3}} {N : Type.{u1}} {M' : Type.{u2}} [_inst_1 : NormedField.{u3} R] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u2} M'] [_inst_9 : NormedSpace.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)] {f : ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u3, u2, u1} R M' N _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_3 _inst_9 _inst_6 f) -> (Function.Injective.{succ u2, succ u1} M' N (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) M' (fun (_x : M') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M') => N) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) M' N (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u1 u2, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)))) f))
+ forall {R : Type.{u3}} {N : Type.{u1}} {M' : Type.{u2}} [_inst_1 : NormedField.{u3} R] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u2} M'] [_inst_9 : NormedSpace.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)] {f : ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u3, u2, u1} R M' N _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_3 _inst_9 _inst_6 f) -> (Function.Injective.{succ u2, succ u1} M' N (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) M' (fun (_x : M') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M') => N) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) M' N (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u1 u2, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)))) f))
Case conversion may be inaccurate. Consider using '#align is_conformal_map.injective IsConformalMap.injectiveₓ'. -/
protected theorem injective {f : M' →L[R] N} (h : IsConformalMap f) : Function.Injective f :=
by
@@ -151,7 +151,7 @@ protected theorem injective {f : M' →L[R] N} (h : IsConformalMap f) : Function
lean 3 declaration is
forall {R : Type.{u1}} {N : Type.{u2}} {M' : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_3 : SeminormedAddCommGroup.{u2} N] [_inst_6 : NormedSpace.{u1, u2} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u3} M'] [_inst_9 : NormedSpace.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)] [_inst_10 : Nontrivial.{u3} M'] {f' : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u1, u3, u2} R M' N _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_3 _inst_9 _inst_6 f') -> (Ne.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) f' (OfNat.ofNat.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) 0 (OfNat.mk.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) 0 (Zero.zero.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6))))))
but is expected to have type
- forall {R : Type.{u2}} {N : Type.{u1}} {M' : Type.{u3}} [_inst_1 : NormedField.{u2} R] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_6 : NormedSpace.{u2, u1} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u3} M'] [_inst_9 : NormedSpace.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)] [_inst_10 : Nontrivial.{u3} M'] {f' : ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u2, u3, u1} R M' N _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_3 _inst_9 _inst_6 f') -> (Ne.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) f' (OfNat.ofNat.{max u1 u3} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) 0 (Zero.toOfNat0.{max u1 u3} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)))))
+ forall {R : Type.{u2}} {N : Type.{u1}} {M' : Type.{u3}} [_inst_1 : NormedField.{u2} R] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_6 : NormedSpace.{u2, u1} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u3} M'] [_inst_9 : NormedSpace.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)] [_inst_10 : Nontrivial.{u3} M'] {f' : ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u2, u3, u1} R M' N _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_3 _inst_9 _inst_6 f') -> (Ne.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) f' (OfNat.ofNat.{max u1 u3} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) 0 (Zero.toOfNat0.{max u1 u3} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)))))
Case conversion may be inaccurate. Consider using '#align is_conformal_map.ne_zero IsConformalMap.ne_zeroₓ'. -/
theorem ne_zero [Nontrivial M'] {f' : M' →L[R] N} (hf' : IsConformalMap f') : f' ≠ 0 :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
! This file was ported from Lean 3 source module analysis.normed_space.conformal_linear_map
-! leanprover-community/mathlib commit d1bd9c5df2867c1cb463bc6364446d57bdd9f7f1
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.NormedSpace.LinearIsometry
/-!
# Conformal Linear Maps
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
A continuous linear map between `R`-normed spaces `X` and `Y` `is_conformal_map` if it is
a nonzero multiple of a linear isometry.
mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c
@@ -48,36 +48,68 @@ noncomputable section
open Function LinearIsometry ContinuousLinearMap
+#print IsConformalMap /-
/-- A continuous linear map `f'` is said to be conformal if it's
a nonzero multiple of a linear isometry. -/
def IsConformalMap {R : Type _} {X Y : Type _} [NormedField R] [SeminormedAddCommGroup X]
[SeminormedAddCommGroup Y] [NormedSpace R X] [NormedSpace R Y] (f' : X →L[R] Y) :=
∃ (c : R)(hc : c ≠ 0)(li : X →ₗᵢ[R] Y), f' = c • li.toContinuousLinearMap
#align is_conformal_map IsConformalMap
+-/
variable {R M N G M' : Type _} [NormedField R] [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
[SeminormedAddCommGroup G] [NormedSpace R M] [NormedSpace R N] [NormedSpace R G]
[NormedAddCommGroup M'] [NormedSpace R M'] {f : M →L[R] N} {g : N →L[R] G} {c : R}
+/- warning: is_conformal_map_id -> isConformalMap_id is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2], IsConformalMap.{u1, u2, u2} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (ContinuousLinearMap.id.{u1, u2} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))
+but is expected to have type
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : NormedField.{u2} R] [_inst_2 : SeminormedAddCommGroup.{u1} M] [_inst_5 : NormedSpace.{u2, u1} R M _inst_1 _inst_2], IsConformalMap.{u2, u1, u1} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (ContinuousLinearMap.id.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))
+Case conversion may be inaccurate. Consider using '#align is_conformal_map_id isConformalMap_idₓ'. -/
theorem isConformalMap_id : IsConformalMap (id R M) :=
⟨1, one_ne_zero, id, by simp⟩
#align is_conformal_map_id isConformalMap_id
+/- warning: is_conformal_map.smul -> IsConformalMap.smul is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] {f : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (forall {c : R}, (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))))))) -> (IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (SMul.smul.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (SMulZeroClass.toHasSmul.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddZeroClass.toHasZero.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddMonoid.toAddZeroClass.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (AddCommMonoid.toAddMonoid.{max u2 u3} (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N 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(AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3)))))) (Module.toMulActionWithZero.{u1, max u2 u3} R (ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) 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(NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3))) (ContinuousLinearMap.module.{u1, u1, u1, u2, u3} R R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (smulCommClass_self.{u1, u3} R N (CommRing.toCommMonoid.{u1} R (SeminormedCommRing.toCommRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (Module.toMulActionWithZero.{u1, u3} R N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)))) (ContinuousSMul.continuousConstSMul.{u1, u3} R N (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (SMulZeroClass.toHasSmul.{u1, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (Module.toMulActionWithZero.{u1, u3} R N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6))))) (BoundedSMul.continuousSMul.{u1, u3} R N (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} R N (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R N (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R N (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u3} N (AddMonoid.toAddZeroClass.{u3} N (AddCommMonoid.toAddMonoid.{u3} N (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3))))) (Module.toMulActionWithZero.{u1, u3} R N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6))))) (NormedSpace.boundedSMul.{u1, u3} R N _inst_1 _inst_3 _inst_6))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (LipschitzAdd.continuousAdd.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3) (SubNegMonoid.toAddMonoid.{u3} N (AddGroup.toSubNegMonoid.{u3} N (SeminormedAddGroup.toAddGroup.{u3} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u3} N _inst_3)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u3} N _inst_3))))))) c f)))
+but is expected to have type
+ forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : NormedField.{u3} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] {f : ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (forall {c : R}, (Ne.{succ u3} R c (OfNat.ofNat.{u3} R 0 (Zero.toOfNat0.{u3} R (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))))) -> (IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (HSMul.hSMul.{u3, max u2 u1, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (instHSMul.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (SMulZeroClass.toSMul.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (SMulWithZero.toSMulZeroClass.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (MulActionWithZero.toSMulWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (ContinuousLinearMap.zero.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (Module.toMulActionWithZero.{u3, max u2 u1} R (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} N _inst_3))) (ContinuousLinearMap.module.{u3, u3, u3, u2, u1} R R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (smulCommClass_self.{u3, u1} R N (CommRing.toCommMonoid.{u3} R (EuclideanDomain.toCommRing.{u3} R (Field.toEuclideanDomain.{u3} R (NormedField.toField.{u3} R _inst_1)))) (MulActionWithZero.toMulAction.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)))) (ContinuousSMul.continuousConstSMul.{u3, u1} R N (UniformSpace.toTopologicalSpace.{u3} R (PseudoMetricSpace.toUniformSpace.{u3} R (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (BoundedSMul.continuousSMul.{u3, u1} R N (SeminormedRing.toPseudoMetricSpace.{u3} R (SeminormedCommRing.toSeminormedRing.{u3} R (NormedCommRing.toSeminormedCommRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3) (CommMonoidWithZero.toZero.{u3} R (CommGroupWithZero.toCommMonoidWithZero.{u3} R (Semifield.toCommGroupWithZero.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (NegZeroClass.toZero.{u1} N (SubNegZeroMonoid.toNegZeroClass.{u1} N (SubtractionMonoid.toSubNegZeroMonoid.{u1} N (SubtractionCommMonoid.toSubtractionMonoid.{u1} N (AddCommGroup.toDivisionAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))))) (SMulZeroClass.toSMul.{u3, u1} R N (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (SMulWithZero.toSMulZeroClass.{u3, u1} R N (MonoidWithZero.toZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (MulActionWithZero.toSMulWithZero.{u3, u1} R N (Semiring.toMonoidWithZero.{u3} R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1))))) (AddMonoid.toZero.{u1} N (AddCommMonoid.toAddMonoid.{u1} N (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)))) (Module.toMulActionWithZero.{u3, u1} R N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6))))) (NormedSpace.boundedSMul.{u3, u1} R N _inst_1 _inst_3 _inst_6))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) (TopologicalAddGroup.toContinuousAdd.{u1} N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (SeminormedAddGroup.toAddGroup.{u1} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} N _inst_3)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} N _inst_3)))))))) c f)))
+Case conversion may be inaccurate. Consider using '#align is_conformal_map.smul IsConformalMap.smulₓ'. -/
theorem IsConformalMap.smul (hf : IsConformalMap f) {c : R} (hc : c ≠ 0) : IsConformalMap (c • f) :=
by
rcases hf with ⟨c', hc', li, rfl⟩
exact ⟨c * c', mul_ne_zero hc hc', li, smul_smul _ _ _⟩
#align is_conformal_map.smul IsConformalMap.smul
+/- warning: is_conformal_map_const_smul -> isConformalMap_const_smul is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] {c : R}, (Ne.{succ u1} R c (OfNat.ofNat.{u1} R 0 (OfNat.mk.{u1} R 0 (Zero.zero.{u1} R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))))))) -> (IsConformalMap.{u1, u2, u2} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (SMul.smul.{u1, u2} R (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (SMulZeroClass.toHasSmul.{u1, u2} R (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddZeroClass.toHasZero.{u2} (ContinuousLinearMap.{u1, u1, u2, 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(AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddMonoid.toAddZeroClass.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M 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(NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (AddCommMonoid.toAddMonoid.{u2} (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (LipschitzAdd.continuousAdd.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} M _inst_2)))))) (Module.toMulActionWithZero.{u1, u2} R (ContinuousLinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (ContinuousLinearMap.addCommMonoid.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (LipschitzAdd.continuousAdd.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} M _inst_2))) (ContinuousLinearMap.module.{u1, u1, u1, u2, u2} R R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (smulCommClass_self.{u1, u2} R M (CommRing.toCommMonoid.{u1} R (SeminormedCommRing.toCommRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5)))) (ContinuousSMul.continuousConstSMul.{u1, u2} R M (UniformSpace.toTopologicalSpace.{u1} R (PseudoMetricSpace.toUniformSpace.{u1} R (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))))) (BoundedSMul.continuousSMul.{u1, u2} R M (SeminormedRing.toPseudoMetricSpace.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R (NormedCommRing.toSeminormedCommRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonUnitalNonAssocRing.{u1} R (Ring.toNonAssocRing.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2))))) (Module.toMulActionWithZero.{u1, u2} R M (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))))) (NormedSpace.boundedSMul.{u1, u2} R M _inst_1 _inst_2 _inst_5))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (LipschitzAdd.continuousAdd.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2) (SubNegMonoid.toAddMonoid.{u2} M (AddGroup.toSubNegMonoid.{u2} M (SeminormedAddGroup.toAddGroup.{u2} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} M _inst_2)))) (SeminormedAddCommGroup.to_lipschitzAdd.{u2} M _inst_2))))))) c (ContinuousLinearMap.id.{u1, u2} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5))))
+but is expected to have type
+ forall {R : Type.{u2}} {M : Type.{u1}} [_inst_1 : NormedField.{u2} R] [_inst_2 : SeminormedAddCommGroup.{u1} M] [_inst_5 : NormedSpace.{u2, u1} R M _inst_1 _inst_2] {c : R}, (Ne.{succ u2} R c (OfNat.ofNat.{u2} R 0 (Zero.toOfNat0.{u2} R (CommMonoidWithZero.toZero.{u2} R (CommGroupWithZero.toCommMonoidWithZero.{u2} R (Semifield.toCommGroupWithZero.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))))) -> (IsConformalMap.{u2, u1, u1} R M M _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (HSMul.hSMul.{u2, u1, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (instHSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Algebra.toSMul.{u2, u1} R (ContinuousLinearMap.{u2, u2, u1, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (Semiring.toNonAssocSemiring.{u2} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5)) (Semifield.toCommSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))) (ContinuousLinearMap.semiring.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (TopologicalAddGroup.toContinuousAdd.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_2)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_2))) (ContinuousLinearMap.algebra.{u2, u1} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_2) (ContinuousSMul.continuousConstSMul.{u2, u1} R M (UniformSpace.toTopologicalSpace.{u2} R (PseudoMetricSpace.toUniformSpace.{u2} R (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (BoundedSMul.continuousSMul.{u2, u1} R M (SeminormedRing.toPseudoMetricSpace.{u2} R (SeminormedCommRing.toSeminormedRing.{u2} R (NormedCommRing.toSeminormedCommRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2) (CommMonoidWithZero.toZero.{u2} R (CommGroupWithZero.toCommMonoidWithZero.{u2} R (Semifield.toCommGroupWithZero.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulZeroClass.toSMul.{u2, u1} R M (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (SMulWithZero.toSMulZeroClass.{u2, u1} R M (CommMonoidWithZero.toZero.{u2} R (CommSemiring.toCommMonoidWithZero.{u2} R (CommRing.toCommSemiring.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (MulActionWithZero.toSMulWithZero.{u2, u1} R M (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1)))))) (NegZeroClass.toZero.{u1} M (SubNegZeroMonoid.toNegZeroClass.{u1} M (SubtractionMonoid.toSubNegZeroMonoid.{u1} M (SubtractionCommMonoid.toSubtractionMonoid.{u1} M (AddCommGroup.toDivisionAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)))))) (Module.toMulActionWithZero.{u2, u1} R M (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R (EuclideanDomain.toCommRing.{u2} R (Field.toEuclideanDomain.{u2} R (NormedField.toField.{u2} R _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))) (NormedSpace.boundedSMul.{u2, u1} R M _inst_1 _inst_2 _inst_5)))))) c (ContinuousLinearMap.id.{u2, u1} R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) (NormedSpace.toModule.{u2, u1} R M _inst_1 _inst_2 _inst_5))))
+Case conversion may be inaccurate. Consider using '#align is_conformal_map_const_smul isConformalMap_const_smulₓ'. -/
theorem isConformalMap_const_smul (hc : c ≠ 0) : IsConformalMap (c • id R M) :=
isConformalMap_id.smul hc
#align is_conformal_map_const_smul isConformalMap_const_smul
+/- warning: linear_isometry.is_conformal_map -> LinearIsometry.isConformalMap is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] (f' : LinearIsometry.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M N _inst_2 _inst_3 (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (LinearIsometry.toContinuousLinearMap.{u1, u1, u2, u3} R R M N (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) _inst_2 _inst_3 (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) f')
+but is expected to have type
+ forall {R : Type.{u3}} {M : Type.{u2}} {N : Type.{u1}} [_inst_1 : NormedField.{u3} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u3, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] (f' : LinearIsometry.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M N _inst_2 _inst_3 (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u3, u2, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 (LinearIsometry.toContinuousLinearMap.{u3, u3, u2, u1} R R M N (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) _inst_2 _inst_3 (NormedSpace.toModule.{u3, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) f')
+Case conversion may be inaccurate. Consider using '#align linear_isometry.is_conformal_map LinearIsometry.isConformalMapₓ'. -/
protected theorem LinearIsometry.isConformalMap (f' : M →ₗᵢ[R] N) :
IsConformalMap f'.toContinuousLinearMap :=
⟨1, one_ne_zero, f', (one_smul _ _).symm⟩
#align linear_isometry.is_conformal_map LinearIsometry.isConformalMap
+/- warning: is_conformal_map_of_subsingleton -> isConformalMap_of_subsingleton is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] [_inst_10 : Subsingleton.{succ u2} M] (f' : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f'
+but is expected to have type
+ forall {R : Type.{u2}} {M : Type.{u3}} {N : Type.{u1}} [_inst_1 : NormedField.{u2} R] [_inst_2 : SeminormedAddCommGroup.{u3} M] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_5 : NormedSpace.{u2, u3} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u2, u1} R N _inst_1 _inst_3] [_inst_10 : Subsingleton.{succ u3} M] (f' : ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u3} M (PseudoMetricSpace.toUniformSpace.{u3} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u3} M (SeminormedAddCommGroup.toAddCommGroup.{u3} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)), IsConformalMap.{u2, u3, u1} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f'
+Case conversion may be inaccurate. Consider using '#align is_conformal_map_of_subsingleton isConformalMap_of_subsingletonₓ'. -/
@[nontriviality]
theorem isConformalMap_of_subsingleton [Subsingleton M] (f' : M →L[R] N) : IsConformalMap f' :=
⟨1, one_ne_zero, ⟨0, fun x => by simp [Subsingleton.elim x 0]⟩, Subsingleton.elim _ _⟩
@@ -85,6 +117,12 @@ theorem isConformalMap_of_subsingleton [Subsingleton M] (f' : M →L[R] N) : IsC
namespace IsConformalMap
+/- warning: is_conformal_map.comp -> IsConformalMap.comp is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {M : Type.{u2}} {N : Type.{u3}} {G : Type.{u4}} [_inst_1 : NormedField.{u1} R] [_inst_2 : SeminormedAddCommGroup.{u2} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_4 : SeminormedAddCommGroup.{u4} G] [_inst_5 : NormedSpace.{u1, u2} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u1, u3} R N _inst_1 _inst_3] [_inst_7 : NormedSpace.{u1, u4} R G _inst_1 _inst_4] {f : ContinuousLinearMap.{u1, u1, u2, u3} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6)} {g : ContinuousLinearMap.{u1, u1, u3, u4} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u4} G (PseudoMetricSpace.toUniformSpace.{u4} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u4} G (SeminormedAddCommGroup.toAddCommGroup.{u4} G _inst_4)) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u1, u4} R G _inst_1 _inst_4 _inst_7)}, (IsConformalMap.{u1, u3, u4} R N G _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g) -> (IsConformalMap.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (IsConformalMap.{u1, u2, u4} R M G _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u4} R R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u2} M (PseudoMetricSpace.toUniformSpace.{u2} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u4} G (PseudoMetricSpace.toUniformSpace.{u4} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u4} G (SeminormedAddCommGroup.toAddCommGroup.{u4} G _inst_4)) (NormedSpace.toModule.{u1, u2} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u1, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u1, u4} R G _inst_1 _inst_4 _inst_7) (RingHomCompTriple.right_ids.{u1, u1} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1))))))) g f))
+but is expected to have type
+ forall {R : Type.{u4}} {M : Type.{u1}} {N : Type.{u3}} {G : Type.{u2}} [_inst_1 : NormedField.{u4} R] [_inst_2 : SeminormedAddCommGroup.{u1} M] [_inst_3 : SeminormedAddCommGroup.{u3} N] [_inst_4 : SeminormedAddCommGroup.{u2} G] [_inst_5 : NormedSpace.{u4, u1} R M _inst_1 _inst_2] [_inst_6 : NormedSpace.{u4, u3} R N _inst_1 _inst_3] [_inst_7 : NormedSpace.{u4, u2} R G _inst_1 _inst_4] {f : ContinuousLinearMap.{u4, u4, u1, u3} R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) (NormedSpace.toModule.{u4, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u4, u3} R N _inst_1 _inst_3 _inst_6)} {g : ContinuousLinearMap.{u4, u4, u3, u2} R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1)))))) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} G (SeminormedAddCommGroup.toAddCommGroup.{u2} G _inst_4)) (NormedSpace.toModule.{u4, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u4, u2} R G _inst_1 _inst_4 _inst_7)}, (IsConformalMap.{u4, u3, u2} R N G _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g) -> (IsConformalMap.{u4, u1, u3} R M N _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (IsConformalMap.{u4, u1, u2} R M G _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (ContinuousLinearMap.comp.{u4, u4, u4, u1, u3, u2} R R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1)))))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1)))))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1)))))) M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_2))) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_2)) N (UniformSpace.toTopologicalSpace.{u3} N (PseudoMetricSpace.toUniformSpace.{u3} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u3} N (SeminormedAddCommGroup.toAddCommGroup.{u3} N _inst_3)) G (UniformSpace.toTopologicalSpace.{u2} G (PseudoMetricSpace.toUniformSpace.{u2} G (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} G _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} G (SeminormedAddCommGroup.toAddCommGroup.{u2} G _inst_4)) (NormedSpace.toModule.{u4, u1} R M _inst_1 _inst_2 _inst_5) (NormedSpace.toModule.{u4, u3} R N _inst_1 _inst_3 _inst_6) (NormedSpace.toModule.{u4, u2} R G _inst_1 _inst_4 _inst_7) (RingHomCompTriple.ids.{u4, u4} R R (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (DivisionSemiring.toSemiring.{u4} R (Semifield.toDivisionSemiring.{u4} R (Field.toSemifield.{u4} R (NormedField.toField.{u4} R _inst_1)))) (RingHom.id.{u4} R (NonAssocRing.toNonAssocSemiring.{u4} R (Ring.toNonAssocRing.{u4} R (NormedRing.toRing.{u4} R (NormedCommRing.toNormedRing.{u4} R (NormedField.toNormedCommRing.{u4} R _inst_1))))))) g f))
+Case conversion may be inaccurate. Consider using '#align is_conformal_map.comp IsConformalMap.compₓ'. -/
theorem comp (hg : IsConformalMap g) (hf : IsConformalMap f) : IsConformalMap (g.comp f) :=
by
rcases hf with ⟨cf, hcf, lif, rfl⟩
@@ -94,12 +132,24 @@ theorem comp (hg : IsConformalMap g) (hf : IsConformalMap f) : IsConformalMap (g
rfl
#align is_conformal_map.comp IsConformalMap.comp
+/- warning: is_conformal_map.injective -> IsConformalMap.injective is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {N : Type.{u2}} {M' : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_3 : SeminormedAddCommGroup.{u2} N] [_inst_6 : NormedSpace.{u1, u2} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u3} M'] [_inst_9 : NormedSpace.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)] {f : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u1, u3, u2} R M' N _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_3 _inst_9 _inst_6 f) -> (Function.Injective.{succ u3, succ u2} M' N (coeFn.{max (succ u3) (succ u2), max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) (fun (_x : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) => M' -> N) (ContinuousLinearMap.toFun.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) f))
+but is expected to have type
+ forall {R : Type.{u3}} {N : Type.{u1}} {M' : Type.{u2}} [_inst_1 : NormedField.{u3} R] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_6 : NormedSpace.{u3, u1} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u2} M'] [_inst_9 : NormedSpace.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)] {f : ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u3, u2, u1} R M' N _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_3 _inst_9 _inst_6 f) -> (Function.Injective.{succ u2, succ u1} M' N (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) M' (fun (_x : M') => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : M') => N) _x) (ContinuousMapClass.toFunLike.{max u1 u2, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) M' N (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u1 u2, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)) R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} R R (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (DivisionSemiring.toSemiring.{u3} R (Semifield.toDivisionSemiring.{u3} R (Field.toSemifield.{u3} R (NormedField.toField.{u3} R _inst_1)))) (RingHom.id.{u3} R (NonAssocRing.toNonAssocSemiring.{u3} R (Ring.toNonAssocRing.{u3} R (NormedRing.toRing.{u3} R (NormedCommRing.toNormedRing.{u3} R (NormedField.toNormedCommRing.{u3} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u2} M' (PseudoMetricSpace.toUniformSpace.{u2} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} M' (NormedAddCommGroup.toAddCommGroup.{u2} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u3, u2} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} M' _inst_8) _inst_9) (NormedSpace.toModule.{u3, u1} R N _inst_1 _inst_3 _inst_6)))) f))
+Case conversion may be inaccurate. Consider using '#align is_conformal_map.injective IsConformalMap.injectiveₓ'. -/
protected theorem injective {f : M' →L[R] N} (h : IsConformalMap f) : Function.Injective f :=
by
rcases h with ⟨c, hc, li, rfl⟩
exact (smul_right_injective _ hc).comp li.injective
#align is_conformal_map.injective IsConformalMap.injective
+/- warning: is_conformal_map.ne_zero -> IsConformalMap.ne_zero is a dubious translation:
+lean 3 declaration is
+ forall {R : Type.{u1}} {N : Type.{u2}} {M' : Type.{u3}} [_inst_1 : NormedField.{u1} R] [_inst_3 : SeminormedAddCommGroup.{u2} N] [_inst_6 : NormedSpace.{u1, u2} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u3} M'] [_inst_9 : NormedSpace.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)] [_inst_10 : Nontrivial.{u3} M'] {f' : ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u1, u3, u2} R M' N _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_3 _inst_9 _inst_6 f') -> (Ne.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) f' (OfNat.ofNat.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) 0 (OfNat.mk.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) 0 (Zero.zero.{max u3 u2} (ContinuousLinearMap.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u1, u1, u3, u2} R R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (NormedRing.toRing.{u1} R (NormedCommRing.toNormedRing.{u1} R (NormedField.toNormedCommRing.{u1} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u2} N (PseudoMetricSpace.toUniformSpace.{u2} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)) (NormedSpace.toModule.{u1, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u1, u2} R N _inst_1 _inst_3 _inst_6))))))
+but is expected to have type
+ forall {R : Type.{u2}} {N : Type.{u1}} {M' : Type.{u3}} [_inst_1 : NormedField.{u2} R] [_inst_3 : SeminormedAddCommGroup.{u1} N] [_inst_6 : NormedSpace.{u2, u1} R N _inst_1 _inst_3] [_inst_8 : NormedAddCommGroup.{u3} M'] [_inst_9 : NormedSpace.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)] [_inst_10 : Nontrivial.{u3} M'] {f' : ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)}, (IsConformalMap.{u2, u3, u1} R M' N _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_3 _inst_9 _inst_6 f') -> (Ne.{max (succ u1) (succ u3)} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) f' (OfNat.ofNat.{max u1 u3} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) 0 (Zero.toOfNat0.{max u1 u3} (ContinuousLinearMap.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)) (ContinuousLinearMap.zero.{u2, u2, u3, u1} R R (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (DivisionSemiring.toSemiring.{u2} R (Semifield.toDivisionSemiring.{u2} R (Field.toSemifield.{u2} R (NormedField.toField.{u2} R _inst_1)))) (RingHom.id.{u2} R (NonAssocRing.toNonAssocSemiring.{u2} R (Ring.toNonAssocRing.{u2} R (NormedRing.toRing.{u2} R (NormedCommRing.toNormedRing.{u2} R (NormedField.toNormedCommRing.{u2} R _inst_1)))))) M' (UniformSpace.toTopologicalSpace.{u3} M' (PseudoMetricSpace.toUniformSpace.{u3} M' (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} M' (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8)))) (AddCommGroup.toAddCommMonoid.{u3} M' (NormedAddCommGroup.toAddCommGroup.{u3} M' _inst_8)) N (UniformSpace.toTopologicalSpace.{u1} N (PseudoMetricSpace.toUniformSpace.{u1} N (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} N _inst_3))) (AddCommGroup.toAddCommMonoid.{u1} N (SeminormedAddCommGroup.toAddCommGroup.{u1} N _inst_3)) (NormedSpace.toModule.{u2, u3} R M' _inst_1 (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} M' _inst_8) _inst_9) (NormedSpace.toModule.{u2, u1} R N _inst_1 _inst_3 _inst_6)))))
+Case conversion may be inaccurate. Consider using '#align is_conformal_map.ne_zero IsConformalMap.ne_zeroₓ'. -/
theorem ne_zero [Nontrivial M'] {f' : M' →L[R] N} (hf' : IsConformalMap f') : f' ≠ 0 :=
by
rintro rfl
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
∃ x ∈ s, p x
instead of ∃ x (_ : x ∈ s), p x
(#9326)
This is a follow-up to #9215. It changes the following theorems and definitions:
IsOpen.exists_subset_affineIndependent_span_eq_top
IsConformalMap
SimpleGraph.induce_connected_of_patches
Submonoid.exists_list_of_mem_closure
AddSubmonoid.exists_list_of_mem_closure
AffineSubspace.mem_affineSpan_insert_iff
AffineBasis.exists_affine_subbasis
exists_affineIndependent
LinearMap.mem_submoduleImage
Basis.basis_singleton_iff
atom_iff_nonzero_span
finrank_eq_one_iff'
Submodule.basis_of_pid_aux
exists_linearIndependent_extension
exists_linearIndependent
countable_cover_nhdsWithin_of_sigma_compact
mem_residual
Also deprecate ENNReal.exists_ne_top'
.
@@ -48,7 +48,7 @@ open Function LinearIsometry ContinuousLinearMap
a nonzero multiple of a linear isometry. -/
def IsConformalMap {R : Type*} {X Y : Type*} [NormedField R] [SeminormedAddCommGroup X]
[SeminormedAddCommGroup Y] [NormedSpace R X] [NormedSpace R Y] (f' : X →L[R] Y) :=
- ∃ (c : R) (_ : c ≠ 0) (li : X →ₗᵢ[R] Y), f' = c • li.toContinuousLinearMap
+ ∃ c ≠ (0 : R), ∃ li : X →ₗᵢ[R] Y, f' = c • li.toContinuousLinearMap
#align is_conformal_map IsConformalMap
variable {R M N G M' : Type*} [NormedField R] [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -46,12 +46,12 @@ open Function LinearIsometry ContinuousLinearMap
/-- A continuous linear map `f'` is said to be conformal if it's
a nonzero multiple of a linear isometry. -/
-def IsConformalMap {R : Type _} {X Y : Type _} [NormedField R] [SeminormedAddCommGroup X]
+def IsConformalMap {R : Type*} {X Y : Type*} [NormedField R] [SeminormedAddCommGroup X]
[SeminormedAddCommGroup Y] [NormedSpace R X] [NormedSpace R Y] (f' : X →L[R] Y) :=
∃ (c : R) (_ : c ≠ 0) (li : X →ₗᵢ[R] Y), f' = c • li.toContinuousLinearMap
#align is_conformal_map IsConformalMap
-variable {R M N G M' : Type _} [NormedField R] [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
+variable {R M N G M' : Type*} [NormedField R] [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
[SeminormedAddCommGroup G] [NormedSpace R M] [NormedSpace R N] [NormedSpace R G]
[NormedAddCommGroup M'] [NormedSpace R M'] {f : M →L[R] N} {g : N →L[R] G} {c : R}
@@ -2,15 +2,12 @@
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-
-! This file was ported from Lean 3 source module analysis.normed_space.conformal_linear_map
-! leanprover-community/mathlib commit d1bd9c5df2867c1cb463bc6364446d57bdd9f7f1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Analysis.NormedSpace.Basic
import Mathlib.Analysis.NormedSpace.LinearIsometry
+#align_import analysis.normed_space.conformal_linear_map from "leanprover-community/mathlib"@"d1bd9c5df2867c1cb463bc6364446d57bdd9f7f1"
+
/-!
# Conformal Linear Maps
Now that leanprover/lean4#2210 has been merged, this PR:
set_option synthInstance.etaExperiment true
commands (and some etaExperiment%
term elaborators)set_option maxHeartbeats
commandsCo-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>
@@ -46,7 +46,6 @@ noncomputable section
open Function LinearIsometry ContinuousLinearMap
-set_option synthInstance.etaExperiment true -- Porting note: gets around lean4#2074
/-- A continuous linear map `f'` is said to be conformal if it's
a nonzero multiple of a linear isometry. -/
by
s! (#3825)
This PR puts, with one exception, every single remaining by
that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh
. The exception is when the by
begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.
Essentially this is s/\n *by$/ by/g
, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated by
s".
@@ -63,8 +63,8 @@ theorem isConformalMap_id : IsConformalMap (id R M) :=
⟨1, one_ne_zero, id, by simp⟩
#align is_conformal_map_id isConformalMap_id
-theorem IsConformalMap.smul (hf : IsConformalMap f) {c : R} (hc : c ≠ 0) : IsConformalMap (c • f) :=
- by
+theorem IsConformalMap.smul (hf : IsConformalMap f) {c : R} (hc : c ≠ 0) :
+ IsConformalMap (c • f) := by
rcases hf with ⟨c', hc', li, rfl⟩
exact ⟨c * c', mul_ne_zero hc hc', li, smul_smul _ _ _⟩
#align is_conformal_map.smul IsConformalMap.smul
The unported dependencies are
algebra.order.module
init.core
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file