analysis.calculus.fderiv.linear
β·
Mathlib.Analysis.Calculus.FDeriv.Linear
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/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
-/
-import Analysis.Calculus.Fderiv.Basic
+import Analysis.Calculus.FDeriv.Basic
#align_import analysis.calculus.fderiv.linear from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
-/
-import Mathbin.Analysis.Calculus.Fderiv.Basic
+import Analysis.Calculus.Fderiv.Basic
#align_import analysis.calculus.fderiv.linear from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.calculus.fderiv.linear
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.Calculus.Fderiv.Basic
+#align_import analysis.calculus.fderiv.linear from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
/-!
# The derivative of bounded linear maps
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -64,95 +64,133 @@ There are currently two variants of these in mathlib, the bundled version
predicate `is_bounded_linear_map`). We give statements for both versions. -/
+#print ContinuousLinearMap.hasStrictFDerivAt /-
protected theorem ContinuousLinearMap.hasStrictFDerivAt {x : E} : HasStrictFDerivAt e e x :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFDerivAt
+-/
+#print ContinuousLinearMap.hasFDerivAtFilter /-
protected theorem ContinuousLinearMap.hasFDerivAtFilter : HasFDerivAtFilter e e x L :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
#align continuous_linear_map.has_fderiv_at_filter ContinuousLinearMap.hasFDerivAtFilter
+-/
+#print ContinuousLinearMap.hasFDerivWithinAt /-
protected theorem ContinuousLinearMap.hasFDerivWithinAt : HasFDerivWithinAt e e s x :=
e.HasFDerivAtFilter
#align continuous_linear_map.has_fderiv_within_at ContinuousLinearMap.hasFDerivWithinAt
+-/
+#print ContinuousLinearMap.hasFDerivAt /-
protected theorem ContinuousLinearMap.hasFDerivAt : HasFDerivAt e e x :=
e.HasFDerivAtFilter
#align continuous_linear_map.has_fderiv_at ContinuousLinearMap.hasFDerivAt
+-/
+#print ContinuousLinearMap.differentiableAt /-
@[simp]
protected theorem ContinuousLinearMap.differentiableAt : DifferentiableAt π e x :=
e.HasFDerivAt.DifferentiableAt
#align continuous_linear_map.differentiable_at ContinuousLinearMap.differentiableAt
+-/
+#print ContinuousLinearMap.differentiableWithinAt /-
protected theorem ContinuousLinearMap.differentiableWithinAt : DifferentiableWithinAt π e s x :=
e.DifferentiableAt.DifferentiableWithinAt
#align continuous_linear_map.differentiable_within_at ContinuousLinearMap.differentiableWithinAt
+-/
+#print ContinuousLinearMap.fderiv /-
@[simp]
protected theorem ContinuousLinearMap.fderiv : fderiv π e x = e :=
e.HasFDerivAt.fderiv
#align continuous_linear_map.fderiv ContinuousLinearMap.fderiv
+-/
+#print ContinuousLinearMap.fderivWithin /-
protected theorem ContinuousLinearMap.fderivWithin (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π e s x = e :=
by
rw [DifferentiableAt.fderivWithin e.differentiable_at hxs]
exact e.fderiv
#align continuous_linear_map.fderiv_within ContinuousLinearMap.fderivWithin
+-/
+#print ContinuousLinearMap.differentiable /-
@[simp]
protected theorem ContinuousLinearMap.differentiable : Differentiable π e := fun x =>
e.DifferentiableAt
#align continuous_linear_map.differentiable ContinuousLinearMap.differentiable
+-/
+#print ContinuousLinearMap.differentiableOn /-
protected theorem ContinuousLinearMap.differentiableOn : DifferentiableOn π e s :=
e.Differentiable.DifferentiableOn
#align continuous_linear_map.differentiable_on ContinuousLinearMap.differentiableOn
+-/
+#print IsBoundedLinearMap.hasFDerivAtFilter /-
theorem IsBoundedLinearMap.hasFDerivAtFilter (h : IsBoundedLinearMap π f) :
HasFDerivAtFilter f h.toContinuousLinearMap x L :=
h.toContinuousLinearMap.HasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_at_filter IsBoundedLinearMap.hasFDerivAtFilter
+-/
+#print IsBoundedLinearMap.hasFDerivWithinAt /-
theorem IsBoundedLinearMap.hasFDerivWithinAt (h : IsBoundedLinearMap π f) :
HasFDerivWithinAt f h.toContinuousLinearMap s x :=
h.HasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_within_at IsBoundedLinearMap.hasFDerivWithinAt
+-/
+#print IsBoundedLinearMap.hasFDerivAt /-
theorem IsBoundedLinearMap.hasFDerivAt (h : IsBoundedLinearMap π f) :
HasFDerivAt f h.toContinuousLinearMap x :=
h.HasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_at IsBoundedLinearMap.hasFDerivAt
+-/
+#print IsBoundedLinearMap.differentiableAt /-
theorem IsBoundedLinearMap.differentiableAt (h : IsBoundedLinearMap π f) : DifferentiableAt π f x :=
h.HasFDerivAt.DifferentiableAt
#align is_bounded_linear_map.differentiable_at IsBoundedLinearMap.differentiableAt
+-/
+#print IsBoundedLinearMap.differentiableWithinAt /-
theorem IsBoundedLinearMap.differentiableWithinAt (h : IsBoundedLinearMap π f) :
DifferentiableWithinAt π f s x :=
h.DifferentiableAt.DifferentiableWithinAt
#align is_bounded_linear_map.differentiable_within_at IsBoundedLinearMap.differentiableWithinAt
+-/
+#print IsBoundedLinearMap.fderiv /-
theorem IsBoundedLinearMap.fderiv (h : IsBoundedLinearMap π f) :
fderiv π f x = h.toContinuousLinearMap :=
HasFDerivAt.fderiv h.HasFDerivAt
#align is_bounded_linear_map.fderiv IsBoundedLinearMap.fderiv
+-/
+#print IsBoundedLinearMap.fderivWithin /-
theorem IsBoundedLinearMap.fderivWithin (h : IsBoundedLinearMap π f)
(hxs : UniqueDiffWithinAt π s x) : fderivWithin π f s x = h.toContinuousLinearMap :=
by
rw [DifferentiableAt.fderivWithin h.differentiable_at hxs]
exact h.fderiv
#align is_bounded_linear_map.fderiv_within IsBoundedLinearMap.fderivWithin
+-/
+#print IsBoundedLinearMap.differentiable /-
theorem IsBoundedLinearMap.differentiable (h : IsBoundedLinearMap π f) : Differentiable π f :=
fun x => h.DifferentiableAt
#align is_bounded_linear_map.differentiable IsBoundedLinearMap.differentiable
+-/
+#print IsBoundedLinearMap.differentiableOn /-
theorem IsBoundedLinearMap.differentiableOn (h : IsBoundedLinearMap π f) : DifferentiableOn π f s :=
h.Differentiable.DifferentiableOn
#align is_bounded_linear_map.differentiable_on IsBoundedLinearMap.differentiableOn
+-/
end ContinuousLinearMap
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -26,7 +26,7 @@ bounded linear maps.
open Filter Asymptotics ContinuousLinearMap Set Metric
-open Topology Classical NNReal Filter Asymptotics ENNReal
+open scoped Topology Classical NNReal Filter Asymptotics ENNReal
noncomputable section
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -64,60 +64,36 @@ There are currently two variants of these in mathlib, the bundled version
predicate `is_bounded_linear_map`). We give statements for both versions. -/
-/- warning: continuous_linear_map.has_strict_fderiv_at -> ContinuousLinearMap.hasStrictFDerivAt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFDerivAtβ'. -/
protected theorem ContinuousLinearMap.hasStrictFDerivAt {x : E} : HasStrictFDerivAt e e x :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFDerivAt
-/- warning: continuous_linear_map.has_fderiv_at_filter -> ContinuousLinearMap.hasFDerivAtFilter is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_fderiv_at_filter ContinuousLinearMap.hasFDerivAtFilterβ'. -/
protected theorem ContinuousLinearMap.hasFDerivAtFilter : HasFDerivAtFilter e e x L :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
#align continuous_linear_map.has_fderiv_at_filter ContinuousLinearMap.hasFDerivAtFilter
-/- warning: continuous_linear_map.has_fderiv_within_at -> ContinuousLinearMap.hasFDerivWithinAt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_fderiv_within_at ContinuousLinearMap.hasFDerivWithinAtβ'. -/
protected theorem ContinuousLinearMap.hasFDerivWithinAt : HasFDerivWithinAt e e s x :=
e.HasFDerivAtFilter
#align continuous_linear_map.has_fderiv_within_at ContinuousLinearMap.hasFDerivWithinAt
-/- warning: continuous_linear_map.has_fderiv_at -> ContinuousLinearMap.hasFDerivAt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_fderiv_at ContinuousLinearMap.hasFDerivAtβ'. -/
protected theorem ContinuousLinearMap.hasFDerivAt : HasFDerivAt e e x :=
e.HasFDerivAtFilter
#align continuous_linear_map.has_fderiv_at ContinuousLinearMap.hasFDerivAt
-/- warning: continuous_linear_map.differentiable_at -> ContinuousLinearMap.differentiableAt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable_at ContinuousLinearMap.differentiableAtβ'. -/
@[simp]
protected theorem ContinuousLinearMap.differentiableAt : DifferentiableAt π e x :=
e.HasFDerivAt.DifferentiableAt
#align continuous_linear_map.differentiable_at ContinuousLinearMap.differentiableAt
-/- warning: continuous_linear_map.differentiable_within_at -> ContinuousLinearMap.differentiableWithinAt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable_within_at ContinuousLinearMap.differentiableWithinAtβ'. -/
protected theorem ContinuousLinearMap.differentiableWithinAt : DifferentiableWithinAt π e s x :=
e.DifferentiableAt.DifferentiableWithinAt
#align continuous_linear_map.differentiable_within_at ContinuousLinearMap.differentiableWithinAt
-/- warning: continuous_linear_map.fderiv -> ContinuousLinearMap.fderiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fderiv ContinuousLinearMap.fderivβ'. -/
@[simp]
protected theorem ContinuousLinearMap.fderiv : fderiv π e x = e :=
e.HasFDerivAt.fderiv
#align continuous_linear_map.fderiv ContinuousLinearMap.fderiv
-/- warning: continuous_linear_map.fderiv_within -> ContinuousLinearMap.fderivWithin is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fderiv_within ContinuousLinearMap.fderivWithinβ'. -/
protected theorem ContinuousLinearMap.fderivWithin (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π e s x = e :=
by
@@ -125,86 +101,44 @@ protected theorem ContinuousLinearMap.fderivWithin (hxs : UniqueDiffWithinAt
exact e.fderiv
#align continuous_linear_map.fderiv_within ContinuousLinearMap.fderivWithin
-/- warning: continuous_linear_map.differentiable -> ContinuousLinearMap.differentiable is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable ContinuousLinearMap.differentiableβ'. -/
@[simp]
protected theorem ContinuousLinearMap.differentiable : Differentiable π e := fun x =>
e.DifferentiableAt
#align continuous_linear_map.differentiable ContinuousLinearMap.differentiable
-/- warning: continuous_linear_map.differentiable_on -> ContinuousLinearMap.differentiableOn is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable_on ContinuousLinearMap.differentiableOnβ'. -/
protected theorem ContinuousLinearMap.differentiableOn : DifferentiableOn π e s :=
e.Differentiable.DifferentiableOn
#align continuous_linear_map.differentiable_on ContinuousLinearMap.differentiableOn
-/- warning: is_bounded_linear_map.has_fderiv_at_filter -> IsBoundedLinearMap.hasFDerivAtFilter is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {L : Filter.{u2} E} (h : IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) x L
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {L : Filter.{u2} E} (h : IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) x L
-Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.has_fderiv_at_filter IsBoundedLinearMap.hasFDerivAtFilterβ'. -/
theorem IsBoundedLinearMap.hasFDerivAtFilter (h : IsBoundedLinearMap π f) :
HasFDerivAtFilter f h.toContinuousLinearMap x L :=
h.toContinuousLinearMap.HasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_at_filter IsBoundedLinearMap.hasFDerivAtFilter
-/- warning: is_bounded_linear_map.has_fderiv_within_at -> IsBoundedLinearMap.hasFDerivWithinAt is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (h : IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) s x
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (h : IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) s x
-Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.has_fderiv_within_at IsBoundedLinearMap.hasFDerivWithinAtβ'. -/
theorem IsBoundedLinearMap.hasFDerivWithinAt (h : IsBoundedLinearMap π f) :
HasFDerivWithinAt f h.toContinuousLinearMap s x :=
h.HasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_within_at IsBoundedLinearMap.hasFDerivWithinAt
-/- warning: is_bounded_linear_map.has_fderiv_at -> IsBoundedLinearMap.hasFDerivAt is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (h : IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) x
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} (h : IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) x
-Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.has_fderiv_at IsBoundedLinearMap.hasFDerivAtβ'. -/
theorem IsBoundedLinearMap.hasFDerivAt (h : IsBoundedLinearMap π f) :
HasFDerivAt f h.toContinuousLinearMap x :=
h.HasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_at IsBoundedLinearMap.hasFDerivAt
-/- warning: is_bounded_linear_map.differentiable_at -> IsBoundedLinearMap.differentiableAt is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, (IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E}, (IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
-Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.differentiable_at IsBoundedLinearMap.differentiableAtβ'. -/
theorem IsBoundedLinearMap.differentiableAt (h : IsBoundedLinearMap π f) : DifferentiableAt π f x :=
h.HasFDerivAt.DifferentiableAt
#align is_bounded_linear_map.differentiable_at IsBoundedLinearMap.differentiableAt
-/- warning: is_bounded_linear_map.differentiable_within_at -> IsBoundedLinearMap.differentiableWithinAt is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
-Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.differentiable_within_at IsBoundedLinearMap.differentiableWithinAtβ'. -/
theorem IsBoundedLinearMap.differentiableWithinAt (h : IsBoundedLinearMap π f) :
DifferentiableWithinAt π f s x :=
h.DifferentiableAt.DifferentiableWithinAt
#align is_bounded_linear_map.differentiable_within_at IsBoundedLinearMap.differentiableWithinAt
-/- warning: is_bounded_linear_map.fderiv -> IsBoundedLinearMap.fderiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.fderiv IsBoundedLinearMap.fderivβ'. -/
theorem IsBoundedLinearMap.fderiv (h : IsBoundedLinearMap π f) :
fderiv π f x = h.toContinuousLinearMap :=
HasFDerivAt.fderiv h.HasFDerivAt
#align is_bounded_linear_map.fderiv IsBoundedLinearMap.fderiv
-/- warning: is_bounded_linear_map.fderiv_within -> IsBoundedLinearMap.fderivWithin is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.fderiv_within IsBoundedLinearMap.fderivWithinβ'. -/
theorem IsBoundedLinearMap.fderivWithin (h : IsBoundedLinearMap π f)
(hxs : UniqueDiffWithinAt π s x) : fderivWithin π f s x = h.toContinuousLinearMap :=
by
@@ -212,22 +146,10 @@ theorem IsBoundedLinearMap.fderivWithin (h : IsBoundedLinearMap π f)
exact h.fderiv
#align is_bounded_linear_map.fderiv_within IsBoundedLinearMap.fderivWithin
-/- warning: is_bounded_linear_map.differentiable -> IsBoundedLinearMap.differentiable is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F}, (IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F}, (IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
-Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.differentiable IsBoundedLinearMap.differentiableβ'. -/
theorem IsBoundedLinearMap.differentiable (h : IsBoundedLinearMap π f) : Differentiable π f :=
fun x => h.DifferentiableAt
#align is_bounded_linear_map.differentiable IsBoundedLinearMap.differentiable
-/- warning: is_bounded_linear_map.differentiable_on -> IsBoundedLinearMap.differentiableOn is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
-Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.differentiable_on IsBoundedLinearMap.differentiableOnβ'. -/
theorem IsBoundedLinearMap.differentiableOn (h : IsBoundedLinearMap π f) : DifferentiableOn π f s :=
h.Differentiable.DifferentiableOn
#align is_bounded_linear_map.differentiable_on IsBoundedLinearMap.differentiableOn
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -65,50 +65,35 @@ predicate `is_bounded_linear_map`). We give statements for both versions. -/
/- warning: continuous_linear_map.has_strict_fderiv_at -> ContinuousLinearMap.hasStrictFDerivAt is a dubious translation:
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(NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E}, HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) 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- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π 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E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) e x
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFDerivAtβ'. -/
protected theorem ContinuousLinearMap.hasStrictFDerivAt {x : E} : HasStrictFDerivAt e e x :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFDerivAt
/- warning: continuous_linear_map.has_fderiv_at_filter -> ContinuousLinearMap.hasFDerivAtFilter is a dubious translation:
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(NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E} {L : Filter.{u2} E}, HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E 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(NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) e x L
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E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) e x L
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_fderiv_at_filter ContinuousLinearMap.hasFDerivAtFilterβ'. -/
protected theorem ContinuousLinearMap.hasFDerivAtFilter : HasFDerivAtFilter e e x L :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
#align continuous_linear_map.has_fderiv_at_filter ContinuousLinearMap.hasFDerivAtFilter
/- warning: continuous_linear_map.has_fderiv_within_at -> ContinuousLinearMap.hasFDerivWithinAt is a dubious translation:
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(NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E} {s : Set.{u2} E}, HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E 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(NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) e s x
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- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {x : E} {s : Set.{u2} E}, HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E 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E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) e s x
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_fderiv_within_at ContinuousLinearMap.hasFDerivWithinAtβ'. -/
protected theorem ContinuousLinearMap.hasFDerivWithinAt : HasFDerivWithinAt e e s x :=
e.HasFDerivAtFilter
#align continuous_linear_map.has_fderiv_within_at ContinuousLinearMap.hasFDerivWithinAt
/- warning: continuous_linear_map.has_fderiv_at -> ContinuousLinearMap.hasFDerivAt is a dubious translation:
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(NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E}, HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E 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(NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) e x
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {x : E}, HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) e x
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_fderiv_at ContinuousLinearMap.hasFDerivAtβ'. -/
protected theorem ContinuousLinearMap.hasFDerivAt : HasFDerivAt e e x :=
e.HasFDerivAtFilter
#align continuous_linear_map.has_fderiv_at ContinuousLinearMap.hasFDerivAt
/- warning: continuous_linear_map.differentiable_at -> ContinuousLinearMap.differentiableAt is a dubious translation:
-lean 3 declaration is
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(NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E}, DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E 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(Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) x
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {x : E}, DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E 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E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) x
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable_at ContinuousLinearMap.differentiableAtβ'. -/
@[simp]
protected theorem ContinuousLinearMap.differentiableAt : DifferentiableAt π e x :=
@@ -116,20 +101,14 @@ protected theorem ContinuousLinearMap.differentiableAt : DifferentiableAt π e
#align continuous_linear_map.differentiable_at ContinuousLinearMap.differentiableAt
/- warning: continuous_linear_map.differentiable_within_at -> ContinuousLinearMap.differentiableWithinAt is a dubious translation:
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(NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E} {s : Set.{u2} E}, DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E 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(NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) s x
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π 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E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) s x
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable_within_at ContinuousLinearMap.differentiableWithinAtβ'. -/
protected theorem ContinuousLinearMap.differentiableWithinAt : DifferentiableWithinAt π e s x :=
e.DifferentiableAt.DifferentiableWithinAt
#align continuous_linear_map.differentiable_within_at ContinuousLinearMap.differentiableWithinAt
/- warning: continuous_linear_map.fderiv -> ContinuousLinearMap.fderiv is a dubious translation:
-lean 3 declaration is
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(NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) 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_inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E 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π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) x) e
-but is expected to have type
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) {x : E}, Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π 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π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)))) e) x) e
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fderiv ContinuousLinearMap.fderivβ'. -/
@[simp]
protected theorem ContinuousLinearMap.fderiv : fderiv π e x = e :=
@@ -137,10 +116,7 @@ protected theorem ContinuousLinearMap.fderiv : fderiv π e x = e :=
#align continuous_linear_map.fderiv ContinuousLinearMap.fderiv
/- warning: continuous_linear_map.fderiv_within -> ContinuousLinearMap.fderivWithin is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π 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(NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) s x) e)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fderiv_within ContinuousLinearMap.fderivWithinβ'. -/
protected theorem ContinuousLinearMap.fderivWithin (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π e s x = e :=
@@ -150,10 +126,7 @@ protected theorem ContinuousLinearMap.fderivWithin (hxs : UniqueDiffWithinAt
#align continuous_linear_map.fderiv_within ContinuousLinearMap.fderivWithin
/- warning: continuous_linear_map.differentiable -> ContinuousLinearMap.differentiable is a dubious translation:
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(NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) 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-but is expected to have type
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(Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e)
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable ContinuousLinearMap.differentiableβ'. -/
@[simp]
protected theorem ContinuousLinearMap.differentiable : Differentiable π e := fun x =>
@@ -161,10 +134,7 @@ protected theorem ContinuousLinearMap.differentiable : Differentiable π e :=
#align continuous_linear_map.differentiable ContinuousLinearMap.differentiable
/- warning: continuous_linear_map.differentiable_on -> ContinuousLinearMap.differentiableOn is a dubious translation:
-lean 3 declaration is
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(NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {s : Set.{u2} E}, DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} 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(NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E 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-but is expected to have type
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(NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {s : Set.{u2} E}, DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E 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(SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) s
+<too large>
Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable_on ContinuousLinearMap.differentiableOnβ'. -/
protected theorem ContinuousLinearMap.differentiableOn : DifferentiableOn π e s :=
e.Differentiable.DifferentiableOn
@@ -225,10 +195,7 @@ theorem IsBoundedLinearMap.differentiableWithinAt (h : IsBoundedLinearMap π f
#align is_bounded_linear_map.differentiable_within_at IsBoundedLinearMap.differentiableWithinAt
/- warning: is_bounded_linear_map.fderiv -> IsBoundedLinearMap.fderiv is a dubious translation:
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-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} (h : IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (IsBoundedLinearMap.toContinuousLinearMap.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h)
+<too large>
Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.fderiv IsBoundedLinearMap.fderivβ'. -/
theorem IsBoundedLinearMap.fderiv (h : IsBoundedLinearMap π f) :
fderiv π f x = h.toContinuousLinearMap :=
@@ -236,10 +203,7 @@ theorem IsBoundedLinearMap.fderiv (h : IsBoundedLinearMap π f) :
#align is_bounded_linear_map.fderiv IsBoundedLinearMap.fderiv
/- warning: is_bounded_linear_map.fderiv_within -> IsBoundedLinearMap.fderivWithin is a dubious translation:
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- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (h : IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (IsBoundedLinearMap.toContinuousLinearMap.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (h : IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (IsBoundedLinearMap.toContinuousLinearMap.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h))
+<too large>
Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.fderiv_within IsBoundedLinearMap.fderivWithinβ'. -/
theorem IsBoundedLinearMap.fderivWithin (h : IsBoundedLinearMap π f)
(hxs : UniqueDiffWithinAt π s x) : fderivWithin π f s x = h.toContinuousLinearMap :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
! This file was ported from Lean 3 source module analysis.calculus.fderiv.linear
-! leanprover-community/mathlib commit e3fb84046afd187b710170887195d50bada934ee
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.Calculus.Fderiv.Basic
/-!
# The derivative of bounded linear maps
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
For detailed documentation of the FrΓ©chet derivative,
see the module docstring of `analysis/calculus/fderiv/basic.lean`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -61,36 +61,84 @@ There are currently two variants of these in mathlib, the bundled version
predicate `is_bounded_linear_map`). We give statements for both versions. -/
+/- warning: continuous_linear_map.has_strict_fderiv_at -> ContinuousLinearMap.hasStrictFDerivAt is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E}, HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) e x
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {x : E}, HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) e x
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFDerivAtβ'. -/
protected theorem ContinuousLinearMap.hasStrictFDerivAt {x : E} : HasStrictFDerivAt e e x :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFDerivAt
+/- warning: continuous_linear_map.has_fderiv_at_filter -> ContinuousLinearMap.hasFDerivAtFilter is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E} {L : Filter.{u2} E}, HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) e x L
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {x : E} {L : Filter.{u2} E}, HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) e x L
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_fderiv_at_filter ContinuousLinearMap.hasFDerivAtFilterβ'. -/
protected theorem ContinuousLinearMap.hasFDerivAtFilter : HasFDerivAtFilter e e x L :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
#align continuous_linear_map.has_fderiv_at_filter ContinuousLinearMap.hasFDerivAtFilter
+/- warning: continuous_linear_map.has_fderiv_within_at -> ContinuousLinearMap.hasFDerivWithinAt is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E} {s : Set.{u2} E}, HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) e s x
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {x : E} {s : Set.{u2} E}, HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) e s x
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_fderiv_within_at ContinuousLinearMap.hasFDerivWithinAtβ'. -/
protected theorem ContinuousLinearMap.hasFDerivWithinAt : HasFDerivWithinAt e e s x :=
e.HasFDerivAtFilter
#align continuous_linear_map.has_fderiv_within_at ContinuousLinearMap.hasFDerivWithinAt
+/- warning: continuous_linear_map.has_fderiv_at -> ContinuousLinearMap.hasFDerivAt is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E}, HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) e x
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {x : E}, HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) e x
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.has_fderiv_at ContinuousLinearMap.hasFDerivAtβ'. -/
protected theorem ContinuousLinearMap.hasFDerivAt : HasFDerivAt e e x :=
e.HasFDerivAtFilter
#align continuous_linear_map.has_fderiv_at ContinuousLinearMap.hasFDerivAt
+/- warning: continuous_linear_map.differentiable_at -> ContinuousLinearMap.differentiableAt is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E}, DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) x
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {x : E}, DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) x
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable_at ContinuousLinearMap.differentiableAtβ'. -/
@[simp]
protected theorem ContinuousLinearMap.differentiableAt : DifferentiableAt π e x :=
e.HasFDerivAt.DifferentiableAt
#align continuous_linear_map.differentiable_at ContinuousLinearMap.differentiableAt
+/- warning: continuous_linear_map.differentiable_within_at -> ContinuousLinearMap.differentiableWithinAt is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E} {s : Set.{u2} E}, DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) s x
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {x : E} {s : Set.{u2} E}, DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) s x
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable_within_at ContinuousLinearMap.differentiableWithinAtβ'. -/
protected theorem ContinuousLinearMap.differentiableWithinAt : DifferentiableWithinAt π e s x :=
e.DifferentiableAt.DifferentiableWithinAt
#align continuous_linear_map.differentiable_within_at ContinuousLinearMap.differentiableWithinAt
+/- warning: continuous_linear_map.fderiv -> ContinuousLinearMap.fderiv is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E}, Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) x) e
+but is expected to have type
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u3}} [_inst_2 : NormedAddCommGroup.{u3} E] [_inst_3 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)] {F : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} F] [_inst_5 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) {x : E}, Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u3 u2, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u3 u2, u1, u1, u3, u2} (ContinuousLinearMap.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u1, u1, u3, u2} π π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_4) _inst_5)))) e) x) e
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fderiv ContinuousLinearMap.fderivβ'. -/
@[simp]
protected theorem ContinuousLinearMap.fderiv : fderiv π e x = e :=
e.HasFDerivAt.fderiv
#align continuous_linear_map.fderiv ContinuousLinearMap.fderiv
+/- warning: continuous_linear_map.fderiv_within -> ContinuousLinearMap.fderivWithin is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) s x) e)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) s x) e)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.fderiv_within ContinuousLinearMap.fderivWithinβ'. -/
protected theorem ContinuousLinearMap.fderivWithin (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π e s x = e :=
by
@@ -98,44 +146,98 @@ protected theorem ContinuousLinearMap.fderivWithin (hxs : UniqueDiffWithinAt
exact e.fderiv
#align continuous_linear_map.fderiv_within ContinuousLinearMap.fderivWithin
+/- warning: continuous_linear_map.differentiable -> ContinuousLinearMap.differentiable is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)), Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)), Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e)
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable ContinuousLinearMap.differentiableβ'. -/
@[simp]
protected theorem ContinuousLinearMap.differentiable : Differentiable π e := fun x =>
e.DifferentiableAt
#align continuous_linear_map.differentiable ContinuousLinearMap.differentiable
+/- warning: continuous_linear_map.differentiable_on -> ContinuousLinearMap.differentiableOn is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] (e : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) {s : Set.{u2} E}, DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fun (_x : ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) => E -> F) (ContinuousLinearMap.toFun.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) e) s
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] (e : ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) {s : Set.{u2} E}, DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E (fun (_x : E) => (fun (x._@.Mathlib.Topology.ContinuousFunction.Basic._hyg.699 : E) => F) _x) (ContinuousMapClass.toFunLike.{max u2 u1, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) E F (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (ContinuousSemilinearMapClass.toContinuousMapClass.{max u2 u1, u3, u3, u2, u1} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5) (ContinuousLinearMap.continuousSemilinearMapClass.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)))) e) s
+Case conversion may be inaccurate. Consider using '#align continuous_linear_map.differentiable_on ContinuousLinearMap.differentiableOnβ'. -/
protected theorem ContinuousLinearMap.differentiableOn : DifferentiableOn π e s :=
e.Differentiable.DifferentiableOn
#align continuous_linear_map.differentiable_on ContinuousLinearMap.differentiableOn
+/- warning: is_bounded_linear_map.has_fderiv_at_filter -> IsBoundedLinearMap.hasFDerivAtFilter is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {L : Filter.{u2} E} (h : IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) x L
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {L : Filter.{u2} E} (h : IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) x L
+Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.has_fderiv_at_filter IsBoundedLinearMap.hasFDerivAtFilterβ'. -/
theorem IsBoundedLinearMap.hasFDerivAtFilter (h : IsBoundedLinearMap π f) :
HasFDerivAtFilter f h.toContinuousLinearMap x L :=
h.toContinuousLinearMap.HasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_at_filter IsBoundedLinearMap.hasFDerivAtFilter
+/- warning: is_bounded_linear_map.has_fderiv_within_at -> IsBoundedLinearMap.hasFDerivWithinAt is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (h : IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) s x
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (h : IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) s x
+Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.has_fderiv_within_at IsBoundedLinearMap.hasFDerivWithinAtβ'. -/
theorem IsBoundedLinearMap.hasFDerivWithinAt (h : IsBoundedLinearMap π f) :
HasFDerivWithinAt f h.toContinuousLinearMap s x :=
h.HasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_within_at IsBoundedLinearMap.hasFDerivWithinAt
+/- warning: is_bounded_linear_map.has_fderiv_at -> IsBoundedLinearMap.hasFDerivAt is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (h : IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) x
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} (h : IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f (IsBoundedLinearMap.toContinuousLinearMap.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h) x
+Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.has_fderiv_at IsBoundedLinearMap.hasFDerivAtβ'. -/
theorem IsBoundedLinearMap.hasFDerivAt (h : IsBoundedLinearMap π f) :
HasFDerivAt f h.toContinuousLinearMap x :=
h.HasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_at IsBoundedLinearMap.hasFDerivAt
+/- warning: is_bounded_linear_map.differentiable_at -> IsBoundedLinearMap.differentiableAt is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E}, (IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E}, (IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x)
+Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.differentiable_at IsBoundedLinearMap.differentiableAtβ'. -/
theorem IsBoundedLinearMap.differentiableAt (h : IsBoundedLinearMap π f) : DifferentiableAt π f x :=
h.HasFDerivAt.DifferentiableAt
#align is_bounded_linear_map.differentiable_at IsBoundedLinearMap.differentiableAt
+/- warning: is_bounded_linear_map.differentiable_within_at -> IsBoundedLinearMap.differentiableWithinAt is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E}, (IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x)
+Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.differentiable_within_at IsBoundedLinearMap.differentiableWithinAtβ'. -/
theorem IsBoundedLinearMap.differentiableWithinAt (h : IsBoundedLinearMap π f) :
DifferentiableWithinAt π f s x :=
h.DifferentiableAt.DifferentiableWithinAt
#align is_bounded_linear_map.differentiable_within_at IsBoundedLinearMap.differentiableWithinAt
+/- warning: is_bounded_linear_map.fderiv -> IsBoundedLinearMap.fderiv is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} (h : IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (IsBoundedLinearMap.toContinuousLinearMap.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} (h : IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderiv.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f x) (IsBoundedLinearMap.toContinuousLinearMap.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h)
+Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.fderiv IsBoundedLinearMap.fderivβ'. -/
theorem IsBoundedLinearMap.fderiv (h : IsBoundedLinearMap π f) :
fderiv π f x = h.toContinuousLinearMap :=
HasFDerivAt.fderiv h.HasFDerivAt
#align is_bounded_linear_map.fderiv IsBoundedLinearMap.fderiv
+/- warning: is_bounded_linear_map.fderiv_within -> IsBoundedLinearMap.fderivWithin is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (h : IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u3)} (ContinuousLinearMap.{u1, u1, u2, u3} π π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4) _inst_5)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (IsBoundedLinearMap.toContinuousLinearMap.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {x : E} {s : Set.{u2} E} (h : IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f), (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) s x) -> (Eq.{max (succ u2) (succ u1)} (ContinuousLinearMap.{u3, u3, u2, u1} π π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) E (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_2)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2) _inst_3) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4) _inst_5)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s x) (IsBoundedLinearMap.toContinuousLinearMap.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f h))
+Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.fderiv_within IsBoundedLinearMap.fderivWithinβ'. -/
theorem IsBoundedLinearMap.fderivWithin (h : IsBoundedLinearMap π f)
(hxs : UniqueDiffWithinAt π s x) : fderivWithin π f s x = h.toContinuousLinearMap :=
by
@@ -143,10 +245,22 @@ theorem IsBoundedLinearMap.fderivWithin (h : IsBoundedLinearMap π f)
exact h.fderiv
#align is_bounded_linear_map.fderiv_within IsBoundedLinearMap.fderivWithin
+/- warning: is_bounded_linear_map.differentiable -> IsBoundedLinearMap.differentiable is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F}, (IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F}, (IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f)
+Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.differentiable IsBoundedLinearMap.differentiableβ'. -/
theorem IsBoundedLinearMap.differentiable (h : IsBoundedLinearMap π f) : Differentiable π f :=
fun x => h.DifferentiableAt
#align is_bounded_linear_map.differentiable IsBoundedLinearMap.differentiable
+/- warning: is_bounded_linear_map.differentiable_on -> IsBoundedLinearMap.differentiableOn is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} F] [_inst_5 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (IsBoundedLinearMap.{u1, u2, u3} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] {E : Type.{u2}} [_inst_2 : NormedAddCommGroup.{u2} E] [_inst_3 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_2)] {F : Type.{u1}} [_inst_4 : NormedAddCommGroup.{u1} F] [_inst_5 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_4)] {f : E -> F} {s : Set.{u2} E}, (IsBoundedLinearMap.{u3, u2, u1} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1) E _inst_2 _inst_3 F _inst_4 _inst_5 f) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_2 _inst_3 F _inst_4 _inst_5 f s)
+Case conversion may be inaccurate. Consider using '#align is_bounded_linear_map.differentiable_on IsBoundedLinearMap.differentiableOnβ'. -/
theorem IsBoundedLinearMap.differentiableOn (h : IsBoundedLinearMap π f) : DifferentiableOn π f s :=
h.Differentiable.DifferentiableOn
#align is_bounded_linear_map.differentiable_on IsBoundedLinearMap.differentiableOn
mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952
@@ -61,25 +61,25 @@ There are currently two variants of these in mathlib, the bundled version
predicate `is_bounded_linear_map`). We give statements for both versions. -/
-protected theorem ContinuousLinearMap.hasStrictFderivAt {x : E} : HasStrictFderivAt e e x :=
+protected theorem ContinuousLinearMap.hasStrictFDerivAt {x : E} : HasStrictFDerivAt e e x :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
-#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFderivAt
+#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFDerivAt
-protected theorem ContinuousLinearMap.hasFderivAtFilter : HasFderivAtFilter e e x L :=
+protected theorem ContinuousLinearMap.hasFDerivAtFilter : HasFDerivAtFilter e e x L :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
-#align continuous_linear_map.has_fderiv_at_filter ContinuousLinearMap.hasFderivAtFilter
+#align continuous_linear_map.has_fderiv_at_filter ContinuousLinearMap.hasFDerivAtFilter
-protected theorem ContinuousLinearMap.hasFderivWithinAt : HasFderivWithinAt e e s x :=
- e.HasFderivAtFilter
-#align continuous_linear_map.has_fderiv_within_at ContinuousLinearMap.hasFderivWithinAt
+protected theorem ContinuousLinearMap.hasFDerivWithinAt : HasFDerivWithinAt e e s x :=
+ e.HasFDerivAtFilter
+#align continuous_linear_map.has_fderiv_within_at ContinuousLinearMap.hasFDerivWithinAt
-protected theorem ContinuousLinearMap.hasFderivAt : HasFderivAt e e x :=
- e.HasFderivAtFilter
-#align continuous_linear_map.has_fderiv_at ContinuousLinearMap.hasFderivAt
+protected theorem ContinuousLinearMap.hasFDerivAt : HasFDerivAt e e x :=
+ e.HasFDerivAtFilter
+#align continuous_linear_map.has_fderiv_at ContinuousLinearMap.hasFDerivAt
@[simp]
protected theorem ContinuousLinearMap.differentiableAt : DifferentiableAt π e x :=
- e.HasFderivAt.DifferentiableAt
+ e.HasFDerivAt.DifferentiableAt
#align continuous_linear_map.differentiable_at ContinuousLinearMap.differentiableAt
protected theorem ContinuousLinearMap.differentiableWithinAt : DifferentiableWithinAt π e s x :=
@@ -88,7 +88,7 @@ protected theorem ContinuousLinearMap.differentiableWithinAt : DifferentiableWit
@[simp]
protected theorem ContinuousLinearMap.fderiv : fderiv π e x = e :=
- e.HasFderivAt.fderiv
+ e.HasFDerivAt.fderiv
#align continuous_linear_map.fderiv ContinuousLinearMap.fderiv
protected theorem ContinuousLinearMap.fderivWithin (hxs : UniqueDiffWithinAt π s x) :
@@ -107,23 +107,23 @@ protected theorem ContinuousLinearMap.differentiableOn : DifferentiableOn π e
e.Differentiable.DifferentiableOn
#align continuous_linear_map.differentiable_on ContinuousLinearMap.differentiableOn
-theorem IsBoundedLinearMap.hasFderivAtFilter (h : IsBoundedLinearMap π f) :
- HasFderivAtFilter f h.toContinuousLinearMap x L :=
- h.toContinuousLinearMap.HasFderivAtFilter
-#align is_bounded_linear_map.has_fderiv_at_filter IsBoundedLinearMap.hasFderivAtFilter
+theorem IsBoundedLinearMap.hasFDerivAtFilter (h : IsBoundedLinearMap π f) :
+ HasFDerivAtFilter f h.toContinuousLinearMap x L :=
+ h.toContinuousLinearMap.HasFDerivAtFilter
+#align is_bounded_linear_map.has_fderiv_at_filter IsBoundedLinearMap.hasFDerivAtFilter
-theorem IsBoundedLinearMap.hasFderivWithinAt (h : IsBoundedLinearMap π f) :
- HasFderivWithinAt f h.toContinuousLinearMap s x :=
- h.HasFderivAtFilter
-#align is_bounded_linear_map.has_fderiv_within_at IsBoundedLinearMap.hasFderivWithinAt
+theorem IsBoundedLinearMap.hasFDerivWithinAt (h : IsBoundedLinearMap π f) :
+ HasFDerivWithinAt f h.toContinuousLinearMap s x :=
+ h.HasFDerivAtFilter
+#align is_bounded_linear_map.has_fderiv_within_at IsBoundedLinearMap.hasFDerivWithinAt
-theorem IsBoundedLinearMap.hasFderivAt (h : IsBoundedLinearMap π f) :
- HasFderivAt f h.toContinuousLinearMap x :=
- h.HasFderivAtFilter
-#align is_bounded_linear_map.has_fderiv_at IsBoundedLinearMap.hasFderivAt
+theorem IsBoundedLinearMap.hasFDerivAt (h : IsBoundedLinearMap π f) :
+ HasFDerivAt f h.toContinuousLinearMap x :=
+ h.HasFDerivAtFilter
+#align is_bounded_linear_map.has_fderiv_at IsBoundedLinearMap.hasFDerivAt
theorem IsBoundedLinearMap.differentiableAt (h : IsBoundedLinearMap π f) : DifferentiableAt π f x :=
- h.HasFderivAt.DifferentiableAt
+ h.HasFDerivAt.DifferentiableAt
#align is_bounded_linear_map.differentiable_at IsBoundedLinearMap.differentiableAt
theorem IsBoundedLinearMap.differentiableWithinAt (h : IsBoundedLinearMap π f) :
@@ -133,7 +133,7 @@ theorem IsBoundedLinearMap.differentiableWithinAt (h : IsBoundedLinearMap π f
theorem IsBoundedLinearMap.fderiv (h : IsBoundedLinearMap π f) :
fderiv π f x = h.toContinuousLinearMap :=
- HasFderivAt.fderiv h.HasFderivAt
+ HasFDerivAt.fderiv h.HasFDerivAt
#align is_bounded_linear_map.fderiv IsBoundedLinearMap.fderiv
theorem IsBoundedLinearMap.fderivWithin (h : IsBoundedLinearMap π f)
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -29,25 +29,15 @@ noncomputable section
section
variable {π : Type*} [NontriviallyNormedField π]
-
variable {E : Type*} [NormedAddCommGroup E] [NormedSpace π E]
-
variable {F : Type*} [NormedAddCommGroup F] [NormedSpace π F]
-
variable {G : Type*} [NormedAddCommGroup G] [NormedSpace π G]
-
variable {G' : Type*} [NormedAddCommGroup G'] [NormedSpace π G']
-
variable {f fβ fβ g : E β F}
-
variable {f' fβ' fβ' g' : E βL[π] F}
-
variable (e : E βL[π] F)
-
variable {x : E}
-
variable {s t : Set E}
-
variable {L Lβ Lβ : Filter E}
section ContinuousLinearMap
Basic setup for fun_prop
for Differentiable(At/On/Within) and HasFDeriv(At/Within/Strict).
Mainly consists of marking theorems with fun_prop
attribute but I had to formulate appropriate _pi
and _apply
theorems. Proofs of _apply
theorems can probably be golfed into neater form.
@@ -60,6 +60,7 @@ There are currently two variants of these in mathlib, the bundled version
predicate `IsBoundedLinearMap`). We give statements for both versions. -/
+@[fun_prop]
protected theorem ContinuousLinearMap.hasStrictFDerivAt {x : E} : HasStrictFDerivAt e e x :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFDerivAt
@@ -68,19 +69,22 @@ protected theorem ContinuousLinearMap.hasFDerivAtFilter : HasFDerivAtFilter e e
.of_isLittleO <| (isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
#align continuous_linear_map.has_fderiv_at_filter ContinuousLinearMap.hasFDerivAtFilter
+@[fun_prop]
protected theorem ContinuousLinearMap.hasFDerivWithinAt : HasFDerivWithinAt e e s x :=
e.hasFDerivAtFilter
#align continuous_linear_map.has_fderiv_within_at ContinuousLinearMap.hasFDerivWithinAt
+@[fun_prop]
protected theorem ContinuousLinearMap.hasFDerivAt : HasFDerivAt e e x :=
e.hasFDerivAtFilter
#align continuous_linear_map.has_fderiv_at ContinuousLinearMap.hasFDerivAt
-@[simp]
+@[simp, fun_prop]
protected theorem ContinuousLinearMap.differentiableAt : DifferentiableAt π e x :=
e.hasFDerivAt.differentiableAt
#align continuous_linear_map.differentiable_at ContinuousLinearMap.differentiableAt
+@[fun_prop]
protected theorem ContinuousLinearMap.differentiableWithinAt : DifferentiableWithinAt π e s x :=
e.differentiableAt.differentiableWithinAt
#align continuous_linear_map.differentiable_within_at ContinuousLinearMap.differentiableWithinAt
@@ -96,11 +100,12 @@ protected theorem ContinuousLinearMap.fderivWithin (hxs : UniqueDiffWithinAt
exact e.fderiv
#align continuous_linear_map.fderiv_within ContinuousLinearMap.fderivWithin
-@[simp]
+@[simp, fun_prop]
protected theorem ContinuousLinearMap.differentiable : Differentiable π e := fun _ =>
e.differentiableAt
#align continuous_linear_map.differentiable ContinuousLinearMap.differentiable
+@[fun_prop]
protected theorem ContinuousLinearMap.differentiableOn : DifferentiableOn π e s :=
e.differentiable.differentiableOn
#align continuous_linear_map.differentiable_on ContinuousLinearMap.differentiableOn
@@ -110,20 +115,24 @@ theorem IsBoundedLinearMap.hasFDerivAtFilter (h : IsBoundedLinearMap π f) :
h.toContinuousLinearMap.hasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_at_filter IsBoundedLinearMap.hasFDerivAtFilter
+@[fun_prop]
theorem IsBoundedLinearMap.hasFDerivWithinAt (h : IsBoundedLinearMap π f) :
HasFDerivWithinAt f h.toContinuousLinearMap s x :=
h.hasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_within_at IsBoundedLinearMap.hasFDerivWithinAt
+@[fun_prop]
theorem IsBoundedLinearMap.hasFDerivAt (h : IsBoundedLinearMap π f) :
HasFDerivAt f h.toContinuousLinearMap x :=
h.hasFDerivAtFilter
#align is_bounded_linear_map.has_fderiv_at IsBoundedLinearMap.hasFDerivAt
+@[fun_prop]
theorem IsBoundedLinearMap.differentiableAt (h : IsBoundedLinearMap π f) : DifferentiableAt π f x :=
h.hasFDerivAt.differentiableAt
#align is_bounded_linear_map.differentiable_at IsBoundedLinearMap.differentiableAt
+@[fun_prop]
theorem IsBoundedLinearMap.differentiableWithinAt (h : IsBoundedLinearMap π f) :
DifferentiableWithinAt π f s x :=
h.differentiableAt.differentiableWithinAt
@@ -140,10 +149,12 @@ theorem IsBoundedLinearMap.fderivWithin (h : IsBoundedLinearMap π f)
exact h.fderiv
#align is_bounded_linear_map.fderiv_within IsBoundedLinearMap.fderivWithin
+@[fun_prop]
theorem IsBoundedLinearMap.differentiable (h : IsBoundedLinearMap π f) : Differentiable π f :=
fun _ => h.differentiableAt
#align is_bounded_linear_map.differentiable IsBoundedLinearMap.differentiable
+@[fun_prop]
theorem IsBoundedLinearMap.differentiableOn (h : IsBoundedLinearMap π f) : DifferentiableOn π f s :=
h.differentiable.differentiableOn
#align is_bounded_linear_map.differentiable_on IsBoundedLinearMap.differentiableOn
open Classical
(#11199)
We remove all but one open Classical
s, instead preferring to use open scoped Classical
. The only real side-effect this led to is moving a couple declarations to use Exists.choose
instead of Classical.choose
.
The first few commits are explicitly labelled regex replaces for ease of review.
@@ -21,7 +21,8 @@ bounded linear maps.
open Filter Asymptotics ContinuousLinearMap Set Metric
-open Topology Classical NNReal Filter Asymptotics ENNReal
+open scoped Classical
+open Topology NNReal Filter Asymptotics ENNReal
noncomputable section
structure
(#8907)
This way we can easily change the definition so that it works for topological vector spaces without generalizing any of the theorems right away.
@@ -64,7 +64,7 @@ protected theorem ContinuousLinearMap.hasStrictFDerivAt {x : E} : HasStrictFDeri
#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFDerivAt
protected theorem ContinuousLinearMap.hasFDerivAtFilter : HasFDerivAtFilter e e x L :=
- (isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
+ .of_isLittleO <| (isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
#align continuous_linear_map.has_fderiv_at_filter ContinuousLinearMap.hasFDerivAtFilter
protected theorem ContinuousLinearMap.hasFDerivWithinAt : HasFDerivWithinAt e e s x :=
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -27,15 +27,15 @@ noncomputable section
section
-variable {π : Type _} [NontriviallyNormedField π]
+variable {π : Type*} [NontriviallyNormedField π]
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace π E]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace π E]
-variable {F : Type _} [NormedAddCommGroup F] [NormedSpace π F]
+variable {F : Type*} [NormedAddCommGroup F] [NormedSpace π F]
-variable {G : Type _} [NormedAddCommGroup G] [NormedSpace π G]
+variable {G : Type*} [NormedAddCommGroup G] [NormedSpace π G]
-variable {G' : Type _} [NormedAddCommGroup G'] [NormedSpace π G']
+variable {G' : Type*} [NormedAddCommGroup G'] [NormedSpace π G']
variable {f fβ fβ g : E β F}
@@ -2,15 +2,12 @@
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.calculus.fderiv.linear
-! leanprover-community/mathlib commit e3fb84046afd187b710170887195d50bada934ee
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Analysis.Calculus.FDeriv.Basic
import Mathlib.Analysis.NormedSpace.BoundedLinearMaps
+#align_import analysis.calculus.fderiv.linear from "leanprover-community/mathlib"@"e3fb84046afd187b710170887195d50bada934ee"
+
/-!
# The derivative of bounded linear maps
IsBoundedBilinearMap
(#4239)
Add IsBoundedBilinearMap.toContinuousLinearMap
and use it to golf
proofs by reusing facts about bundled bilinear maps
E βL[π] F βL[π] G
.
IsBoundedBilinearMap.toContinuousLinearMap
.IsBoundedBilinearMap.is_O'
to
IsBoundedBilinearMap.isBigO'
.isBoundedBilinearMap_deriv_coe
to
IsBoundedBilinearMap.deriv_apply
.LinearMap.mkContinuousOfExistsBoundβ
, a bilinear map version
of LinearMap.mkContinuousOfExistsBound
and use it to redefine
LinearMap.mkContinuousβ
. The new definition is definitionally
equal to the old one.Mathlib.Analysis.NormedSpace.OperatorNorm
instead of
Mathlib.Analysis.NormedSpace.BoundedLinearMaps
in
Mathlib.Analysis.Calculus.FDeriv.Basic
.@@ -9,6 +9,7 @@ Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
! if you have ported upstream changes.
-/
import Mathlib.Analysis.Calculus.FDeriv.Basic
+import Mathlib.Analysis.NormedSpace.BoundedLinearMaps
/-!
# The derivative of bounded linear maps
ContinuousLinearMap.hasStrictFderivAt
to
ContinuousLinearMap.hasStrictFDerivAt
.Analysis/Calculus/FDeriv/Basic
.@@ -61,9 +61,9 @@ There are currently two variants of these in mathlib, the bundled version
predicate `IsBoundedLinearMap`). We give statements for both versions. -/
-protected theorem ContinuousLinearMap.hasStrictFderivAt {x : E} : HasStrictFDerivAt e e x :=
+protected theorem ContinuousLinearMap.hasStrictFDerivAt {x : E} : HasStrictFDerivAt e e x :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
-#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFderivAt
+#align continuous_linear_map.has_strict_fderiv_at ContinuousLinearMap.hasStrictFDerivAt
protected theorem ContinuousLinearMap.hasFDerivAtFilter : HasFDerivAtFilter e e x L :=
(isLittleO_zero _ _).congr_left fun x => by simp only [e.map_sub, sub_self]
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