analysis.calculus.fderiv.star
β·
Mathlib.Analysis.Calculus.FDeriv.Star
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
@@ -3,9 +3,9 @@ Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
-import Analysis.Calculus.Fderiv.Linear
-import Analysis.Calculus.Fderiv.Comp
-import Analysis.Calculus.Fderiv.Equiv
+import Analysis.Calculus.FDeriv.Linear
+import Analysis.Calculus.FDeriv.Comp
+import Analysis.Calculus.FDeriv.Equiv
import Analysis.NormedSpace.Star.Basic
#align_import analysis.calculus.fderiv.star from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,10 +3,10 @@ Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
-import Mathbin.Analysis.Calculus.Fderiv.Linear
-import Mathbin.Analysis.Calculus.Fderiv.Comp
-import Mathbin.Analysis.Calculus.Fderiv.Equiv
-import Mathbin.Analysis.NormedSpace.Star.Basic
+import Analysis.Calculus.Fderiv.Linear
+import Analysis.Calculus.Fderiv.Comp
+import Analysis.Calculus.Fderiv.Equiv
+import Analysis.NormedSpace.Star.Basic
#align_import analysis.calculus.fderiv.star from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,17 +2,14 @@
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module analysis.calculus.fderiv.star
-! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.Calculus.Fderiv.Linear
import Mathbin.Analysis.Calculus.Fderiv.Comp
import Mathbin.Analysis.Calculus.Fderiv.Equiv
import Mathbin.Analysis.NormedSpace.Star.Basic
+#align_import analysis.calculus.fderiv.star from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
+
/-!
# Star operations on derivatives
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -49,76 +49,104 @@ variable {s : Set E}
variable {L : Filter E}
+#print HasStrictFDerivAt.star /-
theorem HasStrictFDerivAt.star (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x :=
(starL' π : F βL[π] F).toContinuousLinearMap.HasStrictFDerivAt.comp x h
#align has_strict_fderiv_at.star HasStrictFDerivAt.star
+-/
+#print HasFDerivAtFilter.star /-
theorem HasFDerivAtFilter.star (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x L :=
(starL' π : F βL[π] F).toContinuousLinearMap.HasFDerivAtFilter.comp x h Filter.tendsto_map
#align has_fderiv_at_filter.star HasFDerivAtFilter.star
+-/
+#print HasFDerivWithinAt.star /-
theorem HasFDerivWithinAt.star (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') s x :=
h.unit
#align has_fderiv_within_at.star HasFDerivWithinAt.star
+-/
+#print HasFDerivAt.star /-
theorem HasFDerivAt.star (h : HasFDerivAt f f' x) :
HasFDerivAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x :=
h.unit
#align has_fderiv_at.star HasFDerivAt.star
+-/
+#print DifferentiableWithinAt.star /-
theorem DifferentiableWithinAt.star (h : DifferentiableWithinAt π f s x) :
DifferentiableWithinAt π (fun y => star (f y)) s x :=
h.HasFDerivWithinAt.unit.DifferentiableWithinAt
#align differentiable_within_at.star DifferentiableWithinAt.star
+-/
+#print differentiableWithinAt_star_iff /-
@[simp]
theorem differentiableWithinAt_star_iff :
DifferentiableWithinAt π (fun y => star (f y)) s x β DifferentiableWithinAt π f s x :=
(starL' π : F βL[π] F).comp_differentiableWithinAt_iff
#align differentiable_within_at_star_iff differentiableWithinAt_star_iff
+-/
+#print DifferentiableAt.star /-
theorem DifferentiableAt.star (h : DifferentiableAt π f x) :
DifferentiableAt π (fun y => star (f y)) x :=
h.HasFDerivAt.unit.DifferentiableAt
#align differentiable_at.star DifferentiableAt.star
+-/
+#print differentiableAt_star_iff /-
@[simp]
theorem differentiableAt_star_iff :
DifferentiableAt π (fun y => star (f y)) x β DifferentiableAt π f x :=
(starL' π : F βL[π] F).comp_differentiableAt_iff
#align differentiable_at_star_iff differentiableAt_star_iff
+-/
+#print DifferentiableOn.star /-
theorem DifferentiableOn.star (h : DifferentiableOn π f s) :
DifferentiableOn π (fun y => star (f y)) s := fun x hx => (h x hx).unit
#align differentiable_on.star DifferentiableOn.star
+-/
+#print differentiableOn_star_iff /-
@[simp]
theorem differentiableOn_star_iff :
DifferentiableOn π (fun y => star (f y)) s β DifferentiableOn π f s :=
(starL' π : F βL[π] F).comp_differentiableOn_iff
#align differentiable_on_star_iff differentiableOn_star_iff
+-/
+#print Differentiable.star /-
theorem Differentiable.star (h : Differentiable π f) : Differentiable π fun y => star (f y) :=
fun x => (h x).unit
#align differentiable.star Differentiable.star
+-/
+#print differentiable_star_iff /-
@[simp]
theorem differentiable_star_iff : (Differentiable π fun y => star (f y)) β Differentiable π f :=
(starL' π : F βL[π] F).comp_differentiable_iff
#align differentiable_star_iff differentiable_star_iff
+-/
+#print fderivWithin_star /-
theorem fderivWithin_star (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π (fun y => star (f y)) s x =
((starL' π : F βL[π] F) : F βL[π] F) βL fderivWithin π f s x :=
(starL' π : F βL[π] F).comp_fderivWithin hxs
#align fderiv_within_star fderivWithin_star
+-/
+#print fderiv_star /-
@[simp]
theorem fderiv_star :
fderiv π (fun y => star (f y)) x = ((starL' π : F βL[π] F) : F βL[π] F) βL fderiv π f x :=
(starL' π : F βL[π] F).comp_fderiv
#align fderiv_star fderiv_star
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -28,7 +28,7 @@ star operation; which as should be expected rules out `π = β`.
-/
-open Classical
+open scoped Classical
variable {π : Type _} [NontriviallyNormedField π] [StarRing π] [TrivialStar π]
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -49,115 +49,73 @@ variable {s : Set E}
variable {L : Filter E}
-/- warning: has_strict_fderiv_at.star -> HasStrictFDerivAt.star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.star HasStrictFDerivAt.starβ'. -/
theorem HasStrictFDerivAt.star (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x :=
(starL' π : F βL[π] F).toContinuousLinearMap.HasStrictFDerivAt.comp x h
#align has_strict_fderiv_at.star HasStrictFDerivAt.star
-/- warning: has_fderiv_at_filter.star -> HasFDerivAtFilter.star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.star HasFDerivAtFilter.starβ'. -/
theorem HasFDerivAtFilter.star (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x L :=
(starL' π : F βL[π] F).toContinuousLinearMap.HasFDerivAtFilter.comp x h Filter.tendsto_map
#align has_fderiv_at_filter.star HasFDerivAtFilter.star
-/- warning: has_fderiv_within_at.star -> HasFDerivWithinAt.star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.star HasFDerivWithinAt.starβ'. -/
theorem HasFDerivWithinAt.star (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') s x :=
h.unit
#align has_fderiv_within_at.star HasFDerivWithinAt.star
-/- warning: has_fderiv_at.star -> HasFDerivAt.star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at.star HasFDerivAt.starβ'. -/
theorem HasFDerivAt.star (h : HasFDerivAt f f' x) :
HasFDerivAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x :=
h.unit
#align has_fderiv_at.star HasFDerivAt.star
-/- warning: differentiable_within_at.star -> DifferentiableWithinAt.star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_within_at.star DifferentiableWithinAt.starβ'. -/
theorem DifferentiableWithinAt.star (h : DifferentiableWithinAt π f s x) :
DifferentiableWithinAt π (fun y => star (f y)) s x :=
h.HasFDerivWithinAt.unit.DifferentiableWithinAt
#align differentiable_within_at.star DifferentiableWithinAt.star
-/- warning: differentiable_within_at_star_iff -> differentiableWithinAt_star_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_within_at_star_iff differentiableWithinAt_star_iffβ'. -/
@[simp]
theorem differentiableWithinAt_star_iff :
DifferentiableWithinAt π (fun y => star (f y)) s x β DifferentiableWithinAt π f s x :=
(starL' π : F βL[π] F).comp_differentiableWithinAt_iff
#align differentiable_within_at_star_iff differentiableWithinAt_star_iff
-/- warning: differentiable_at.star -> DifferentiableAt.star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_at.star DifferentiableAt.starβ'. -/
theorem DifferentiableAt.star (h : DifferentiableAt π f x) :
DifferentiableAt π (fun y => star (f y)) x :=
h.HasFDerivAt.unit.DifferentiableAt
#align differentiable_at.star DifferentiableAt.star
-/- warning: differentiable_at_star_iff -> differentiableAt_star_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_at_star_iff differentiableAt_star_iffβ'. -/
@[simp]
theorem differentiableAt_star_iff :
DifferentiableAt π (fun y => star (f y)) x β DifferentiableAt π f x :=
(starL' π : F βL[π] F).comp_differentiableAt_iff
#align differentiable_at_star_iff differentiableAt_star_iff
-/- warning: differentiable_on.star -> DifferentiableOn.star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_on.star DifferentiableOn.starβ'. -/
theorem DifferentiableOn.star (h : DifferentiableOn π f s) :
DifferentiableOn π (fun y => star (f y)) s := fun x hx => (h x hx).unit
#align differentiable_on.star DifferentiableOn.star
-/- warning: differentiable_on_star_iff -> differentiableOn_star_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_on_star_iff differentiableOn_star_iffβ'. -/
@[simp]
theorem differentiableOn_star_iff :
DifferentiableOn π (fun y => star (f y)) s β DifferentiableOn π f s :=
(starL' π : F βL[π] F).comp_differentiableOn_iff
#align differentiable_on_star_iff differentiableOn_star_iff
-/- warning: differentiable.star -> Differentiable.star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable.star Differentiable.starβ'. -/
theorem Differentiable.star (h : Differentiable π f) : Differentiable π fun y => star (f y) :=
fun x => (h x).unit
#align differentiable.star Differentiable.star
-/- warning: differentiable_star_iff -> differentiable_star_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_star_iff differentiable_star_iffβ'. -/
@[simp]
theorem differentiable_star_iff : (Differentiable π fun y => star (f y)) β Differentiable π f :=
(starL' π : F βL[π] F).comp_differentiable_iff
#align differentiable_star_iff differentiable_star_iff
-/- warning: fderiv_within_star -> fderivWithin_star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_within_star fderivWithin_starβ'. -/
theorem fderivWithin_star (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π (fun y => star (f y)) s x =
((starL' π : F βL[π] F) : F βL[π] F) βL fderivWithin π f s x :=
(starL' π : F βL[π] F).comp_fderivWithin hxs
#align fderiv_within_star fderivWithin_star
-/- warning: fderiv_star -> fderiv_star is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align fderiv_star fderiv_starβ'. -/
@[simp]
theorem fderiv_star :
fderiv π (fun y => star (f y)) x = ((starL' π : F βL[π] F) : F βL[π] F) βL fderiv π f x :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -50,10 +50,7 @@ variable {s : Set E}
variable {L : Filter E}
/- warning: has_strict_fderiv_at.star -> HasStrictFDerivAt.star is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) f') x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u1} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u3, u3} 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)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u1} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (starL'.{u3, u1} π F (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) _inst_7 (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) _inst_10)) f') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.star HasStrictFDerivAt.starβ'. -/
theorem HasStrictFDerivAt.star (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x :=
@@ -61,10 +58,7 @@ theorem HasStrictFDerivAt.star (h : HasStrictFDerivAt f f' x) :
#align has_strict_fderiv_at.star HasStrictFDerivAt.star
/- warning: has_fderiv_at_filter.star -> HasFDerivAtFilter.star is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) f') x L)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u1} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u3, u3} 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)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u1} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (starL'.{u3, u1} π F (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) _inst_7 (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) _inst_10)) f') x L)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.star HasFDerivAtFilter.starβ'. -/
theorem HasFDerivAtFilter.star (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x L :=
@@ -72,10 +66,7 @@ theorem HasFDerivAtFilter.star (h : HasFDerivAtFilter f f' x L) :
#align has_fderiv_at_filter.star HasFDerivAtFilter.star
/- warning: has_fderiv_within_at.star -> HasFDerivWithinAt.star is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) f') s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u1} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u3, u3} 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)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u1} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (starL'.{u3, u1} π F (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) _inst_7 (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) _inst_10)) f') s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.star HasFDerivWithinAt.starβ'. -/
theorem HasFDerivWithinAt.star (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') s x :=
@@ -83,10 +74,7 @@ theorem HasFDerivWithinAt.star (h : HasFDerivWithinAt f f' s x) :
#align has_fderiv_within_at.star HasFDerivWithinAt.star
/- warning: has_fderiv_at.star -> HasFDerivAt.star is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) f') x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u1} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u3, u3} 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)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u1} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (starL'.{u3, u1} π F (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) _inst_7 (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) _inst_10)) f') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.star HasFDerivAt.starβ'. -/
theorem HasFDerivAt.star (h : HasFDerivAt f f' x) :
HasFDerivAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x :=
@@ -94,10 +82,7 @@ theorem HasFDerivAt.star (h : HasFDerivAt f f' x) :
#align has_fderiv_at.star HasFDerivAt.star
/- warning: differentiable_within_at.star -> DifferentiableWithinAt.star is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_within_at.star DifferentiableWithinAt.starβ'. -/
theorem DifferentiableWithinAt.star (h : DifferentiableWithinAt π f s x) :
DifferentiableWithinAt π (fun y => star (f y)) s x :=
@@ -105,10 +90,7 @@ theorem DifferentiableWithinAt.star (h : DifferentiableWithinAt π f s x) :
#align differentiable_within_at.star DifferentiableWithinAt.star
/- warning: differentiable_within_at_star_iff -> differentiableWithinAt_star_iff is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, Iff (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) s x) (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, Iff (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) s x) (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_within_at_star_iff differentiableWithinAt_star_iffβ'. -/
@[simp]
theorem differentiableWithinAt_star_iff :
@@ -117,10 +99,7 @@ theorem differentiableWithinAt_star_iff :
#align differentiable_within_at_star_iff differentiableWithinAt_star_iff
/- warning: differentiable_at.star -> DifferentiableAt.star is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) x)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_at.star DifferentiableAt.starβ'. -/
theorem DifferentiableAt.star (h : DifferentiableAt π f x) :
DifferentiableAt π (fun y => star (f y)) x :=
@@ -128,10 +107,7 @@ theorem DifferentiableAt.star (h : DifferentiableAt π f x) :
#align differentiable_at.star DifferentiableAt.star
/- warning: differentiable_at_star_iff -> differentiableAt_star_iff is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {x : E}, Iff (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) x) (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {x : E}, Iff (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) x) (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_at_star_iff differentiableAt_star_iffβ'. -/
@[simp]
theorem differentiableAt_star_iff :
@@ -140,20 +116,14 @@ theorem differentiableAt_star_iff :
#align differentiable_at_star_iff differentiableAt_star_iff
/- warning: differentiable_on.star -> DifferentiableOn.star is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) s)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) s)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_on.star DifferentiableOn.starβ'. -/
theorem DifferentiableOn.star (h : DifferentiableOn π f s) :
DifferentiableOn π (fun y => star (f y)) s := fun x hx => (h x hx).unit
#align differentiable_on.star DifferentiableOn.star
/- warning: differentiable_on_star_iff -> differentiableOn_star_iff is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {s : Set.{u2} E}, Iff (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) s) (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {s : Set.{u2} E}, Iff (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) s) (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_on_star_iff differentiableOn_star_iffβ'. -/
@[simp]
theorem differentiableOn_star_iff :
@@ -162,20 +132,14 @@ theorem differentiableOn_star_iff :
#align differentiable_on_star_iff differentiableOn_star_iff
/- warning: differentiable.star -> Differentiable.star is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)))
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable.star Differentiable.starβ'. -/
theorem Differentiable.star (h : Differentiable π f) : Differentiable π fun y => star (f y) :=
fun x => (h x).unit
#align differentiable.star Differentiable.star
/- warning: differentiable_star_iff -> differentiable_star_iff is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F}, Iff (Differentiable.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y))) (Differentiable.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f)
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F}, Iff (Differentiable.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y))) (Differentiable.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_star_iff differentiable_star_iffβ'. -/
@[simp]
theorem differentiable_star_iff : (Differentiable π fun y => star (f y)) β Differentiable π f :=
@@ -183,10 +147,7 @@ theorem differentiable_star_iff : (Differentiable π fun y => star (f y)) β
#align differentiable_star_iff differentiable_star_iff
/- warning: fderiv_within_star -> fderivWithin_star is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) s x) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x)))
-but is expected to have type
- forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) s x) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u1} π π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u3, u3} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u1} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (starL'.{u3, u1} π F (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) _inst_7 (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) _inst_10)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_within_star fderivWithin_starβ'. -/
theorem fderivWithin_star (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π (fun y => star (f y)) s x =
@@ -195,10 +156,7 @@ theorem fderivWithin_star (hxs : UniqueDiffWithinAt π s x) :
#align fderiv_within_star fderivWithin_star
/- warning: fderiv_star -> fderiv_star is a dubious translation:
-lean 3 declaration is
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) x) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x))
-but is expected to have type
- forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} π (CommRing.toNonUnitalCommRing.{u1} π (EuclideanDomain.toCommRing.{u1} π (Field.toEuclideanDomain.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toStar.{u1} π (StarAddMonoid.toInvolutiveStar.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (Ring.toAddGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} π (CommRing.toNonUnitalCommRing.{u1} π (EuclideanDomain.toCommRing.{u1} π (Field.toEuclideanDomain.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) _inst_2)))] {E : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} E] [_inst_5 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] {F : Type.{u2}} [_inst_6 : NormedAddCommGroup.{u2} F] [_inst_7 : StarAddMonoid.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)] [_inst_9 : StarModule.{u1, u2} π F (InvolutiveStar.toStar.{u1} π (StarAddMonoid.toInvolutiveStar.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (Ring.toAddGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} π (CommRing.toNonUnitalCommRing.{u1} π (EuclideanDomain.toCommRing.{u1} π (Field.toEuclideanDomain.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u2} F (StarAddMonoid.toInvolutiveStar.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u1, u2} π F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π F (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u2} π F (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (InvolutiveStar.toStar.{u2} F (StarAddMonoid.toInvolutiveStar.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_6)))) _inst_7))] {f : E -> F} {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_4)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u2} F (InvolutiveStar.toStar.{u2} F (StarAddMonoid.toInvolutiveStar.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_6)))) _inst_7)) (f y)) x) (ContinuousLinearMap.comp.{u1, u1, u1, u3, u2, u2} π π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{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_4)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u1, u1, u2, u2} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHomInvPair.ids.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (RingHomInvPair.ids.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8) (starL'.{u1, u2} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) _inst_10)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x))
+<too large>
Case conversion may be inaccurate. Consider using '#align fderiv_star fderiv_starβ'. -/
@[simp]
theorem fderiv_star :
mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
! This file was ported from Lean 3 source module analysis.calculus.fderiv.star
-! leanprover-community/mathlib commit ad84a13c884fd19e286fb7abb36f4b9ba7e2f615
+! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -16,6 +16,9 @@ import Mathbin.Analysis.NormedSpace.Star.Basic
/-!
# Star operations on derivatives
+> 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/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -46,73 +46,157 @@ variable {s : Set E}
variable {L : Filter E}
+/- warning: has_strict_fderiv_at.star -> HasStrictFDerivAt.star is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)} {x : E}, (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x) -> (HasStrictFDerivAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) f') x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)} {x : E}, (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x) -> (HasStrictFDerivAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u1} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u3, u3} 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)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u1} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (starL'.{u3, u1} π F (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) _inst_7 (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) _inst_10)) f') x)
+Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.star HasStrictFDerivAt.starβ'. -/
theorem HasStrictFDerivAt.star (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x :=
(starL' π : F βL[π] F).toContinuousLinearMap.HasStrictFDerivAt.comp x h
#align has_strict_fderiv_at.star HasStrictFDerivAt.star
+/- warning: has_fderiv_at_filter.star -> HasFDerivAtFilter.star is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x L) -> (HasFDerivAtFilter.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) f') x L)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)} {x : E} {L : Filter.{u2} E}, (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x L) -> (HasFDerivAtFilter.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u1} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u3, u3} 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)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u1} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (starL'.{u3, u1} π F (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) _inst_7 (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) _inst_10)) f') x L)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.star HasFDerivAtFilter.starβ'. -/
theorem HasFDerivAtFilter.star (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x L :=
(starL' π : F βL[π] F).toContinuousLinearMap.HasFDerivAtFilter.comp x h Filter.tendsto_map
#align has_fderiv_at_filter.star HasFDerivAtFilter.star
+/- warning: has_fderiv_within_at.star -> HasFDerivWithinAt.star is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' s x) -> (HasFDerivWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) f') s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)} {x : E} {s : Set.{u2} E}, (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' s x) -> (HasFDerivWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u1} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u3, u3} 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)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u1} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (starL'.{u3, u1} π F (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) _inst_7 (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) _inst_10)) f') s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.star HasFDerivWithinAt.starβ'. -/
theorem HasFDerivWithinAt.star (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') s x :=
h.unit
#align has_fderiv_within_at.star HasFDerivWithinAt.star
+/- warning: has_fderiv_at.star -> HasFDerivAt.star is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)} {x : E}, (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x) -> (HasFDerivAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) f') x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {f' : 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)} {x : E}, (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f f' x) -> (HasFDerivAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (x : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f x)) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u1} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u3, u3} 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)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u1} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (starL'.{u3, u1} π F (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) _inst_7 (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) _inst_10)) f') x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at.star HasFDerivAt.starβ'. -/
theorem HasFDerivAt.star (h : HasFDerivAt f f' x) :
HasFDerivAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x :=
h.unit
#align has_fderiv_at.star HasFDerivAt.star
+/- warning: differentiable_within_at.star -> DifferentiableWithinAt.star is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x) -> (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x) -> (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at.star DifferentiableWithinAt.starβ'. -/
theorem DifferentiableWithinAt.star (h : DifferentiableWithinAt π f s x) :
DifferentiableWithinAt π (fun y => star (f y)) s x :=
h.HasFDerivWithinAt.unit.DifferentiableWithinAt
#align differentiable_within_at.star DifferentiableWithinAt.star
+/- warning: differentiable_within_at_star_iff -> differentiableWithinAt_star_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, Iff (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) s x) (DifferentiableWithinAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, Iff (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) s x) (DifferentiableWithinAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at_star_iff differentiableWithinAt_star_iffβ'. -/
@[simp]
theorem differentiableWithinAt_star_iff :
DifferentiableWithinAt π (fun y => star (f y)) s x β DifferentiableWithinAt π f s x :=
(starL' π : F βL[π] F).comp_differentiableWithinAt_iff
#align differentiable_within_at_star_iff differentiableWithinAt_star_iff
+/- warning: differentiable_at.star -> DifferentiableAt.star is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {x : E}, (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x) -> (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {x : E}, (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x) -> (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at.star DifferentiableAt.starβ'. -/
theorem DifferentiableAt.star (h : DifferentiableAt π f x) :
DifferentiableAt π (fun y => star (f y)) x :=
h.HasFDerivAt.unit.DifferentiableAt
#align differentiable_at.star DifferentiableAt.star
+/- warning: differentiable_at_star_iff -> differentiableAt_star_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {x : E}, Iff (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) x) (DifferentiableAt.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {x : E}, Iff (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) x) (DifferentiableAt.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at_star_iff differentiableAt_star_iffβ'. -/
@[simp]
theorem differentiableAt_star_iff :
DifferentiableAt π (fun y => star (f y)) x β DifferentiableAt π f x :=
(starL' π : F βL[π] F).comp_differentiableAt_iff
#align differentiable_at_star_iff differentiableAt_star_iff
+/- warning: differentiable_on.star -> DifferentiableOn.star is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s) -> (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {s : Set.{u2} E}, (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s) -> (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on.star DifferentiableOn.starβ'. -/
theorem DifferentiableOn.star (h : DifferentiableOn π f s) :
DifferentiableOn π (fun y => star (f y)) s := fun x hx => (h x hx).unit
#align differentiable_on.star DifferentiableOn.star
+/- warning: differentiable_on_star_iff -> differentiableOn_star_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {s : Set.{u2} E}, Iff (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) s) (DifferentiableOn.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {s : Set.{u2} E}, Iff (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) s) (DifferentiableOn.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on_star_iff differentiableOn_star_iffβ'. -/
@[simp]
theorem differentiableOn_star_iff :
DifferentiableOn π (fun y => star (f y)) s β DifferentiableOn π f s :=
(starL' π : F βL[π] F).comp_differentiableOn_iff
#align differentiable_on_star_iff differentiableOn_star_iff
+/- warning: differentiable.star -> Differentiable.star is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F}, (Differentiable.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f) -> (Differentiable.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F}, (Differentiable.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f) -> (Differentiable.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)))
+Case conversion may be inaccurate. Consider using '#align differentiable.star Differentiable.starβ'. -/
theorem Differentiable.star (h : Differentiable π f) : Differentiable π fun y => star (f y) :=
fun x => (h x).unit
#align differentiable.star Differentiable.star
+/- warning: differentiable_star_iff -> differentiable_star_iff is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F}, Iff (Differentiable.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y))) (Differentiable.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f)
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F}, Iff (Differentiable.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y))) (Differentiable.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f)
+Case conversion may be inaccurate. Consider using '#align differentiable_star_iff differentiable_star_iffβ'. -/
@[simp]
theorem differentiable_star_iff : (Differentiable π fun y => star (f y)) β Differentiable π f :=
(starL' π : F βL[π] F).comp_differentiable_iff
#align differentiable_star_iff differentiable_star_iff
+/- warning: fderiv_within_star -> fderivWithin_star is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u1, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) s x) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) (fderivWithin.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x)))
+but is expected to have type
+ forall {π : Type.{u3}} [_inst_1 : NontriviallyNormedField.{u3} π] [_inst_2 : StarRing.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))] [_inst_3 : TrivialStar.{u3} π (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u1}} [_inst_6 : NormedAddCommGroup.{u1} F] [_inst_7 : StarAddMonoid.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6))))] [_inst_8 : NormedSpace.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)] [_inst_9 : StarModule.{u3, u1} π F (InvolutiveStar.toStar.{u3} π (StarAddMonoid.toInvolutiveStar.{u3} π (AddMonoidWithOne.toAddMonoid.{u3} π (AddGroupWithOne.toAddMonoidWithOne.{u3} π (Ring.toAddGroupWithOne.{u3} π (NormedRing.toRing.{u3} π (NormedCommRing.toNormedRing.{u3} π (NormedField.toNormedCommRing.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (StarRing.toStarAddMonoid.{u3} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u3} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u3} π (CommRing.toNonUnitalCommRing.{u3} π (EuclideanDomain.toCommRing.{u3} π (Field.toEuclideanDomain.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u3, u1} π F (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u3, u1} π F (CommMonoidWithZero.toZero.{u3} π (CommGroupWithZero.toCommMonoidWithZero.{u3} π (Semifield.toCommGroupWithZero.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u3, u1} π F (Semiring.toMonoidWithZero.{u3} π (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (NegZeroClass.toZero.{u1} F (SubNegZeroMonoid.toNegZeroClass.{u1} F (SubtractionMonoid.toSubNegZeroMonoid.{u1} F (SubtractionCommMonoid.toSubtractionMonoid.{u1} F (AddCommGroup.toDivisionAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)))))) (Module.toMulActionWithZero.{u3, u1} π F (DivisionSemiring.toSemiring.{u3} π (Semifield.toDivisionSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u1} F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7))] {f : E -> F} {x : E} {s : Set.{u2} E}, (UniqueDiffWithinAt.{u3, u2} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u2} E (PseudoMetricSpace.toUniformSpace.{u2} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)))) 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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u1} F (InvolutiveStar.toStar.{u1} F (StarAddMonoid.toInvolutiveStar.{u1} F (SubNegMonoid.toAddMonoid.{u1} F (AddGroup.toSubNegMonoid.{u1} F (NormedAddGroup.toAddGroup.{u1} F (NormedAddCommGroup.toNormedAddGroup.{u1} F _inst_6)))) _inst_7)) (f y)) s x) (ContinuousLinearMap.comp.{u3, u3, u3, u2, u1, u1} π π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u2} π E (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u3, u3} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u3, u3, u1, u1} π π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHom.id.{u3} π (Semiring.toNonAssocSemiring.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1))))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) (RingHomInvPair.ids.{u3} π (CommSemiring.toSemiring.{u3} π (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) (starL'.{u3, u1} π F (Semifield.toCommSemiring.{u3} π (Field.toSemifield.{u3} π (NormedField.toField.{u3} π (NontriviallyNormedField.toNormedField.{u3} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u1} F (NormedAddCommGroup.toAddCommGroup.{u1} F _inst_6)) _inst_7 (NormedSpace.toModule.{u3, u1} π F (NontriviallyNormedField.toNormedField.{u3} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u1} F (PseudoMetricSpace.toUniformSpace.{u1} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u1} F _inst_6)))) _inst_10)) (fderivWithin.{u3, u2, u1} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f s x)))
+Case conversion may be inaccurate. Consider using '#align fderiv_within_star fderivWithin_starβ'. -/
theorem fderivWithin_star (hxs : UniqueDiffWithinAt π s x) :
fderivWithin π (fun y => star (f y)) s x =
((starL' π : F βL[π] F) : F βL[π] F) βL fderivWithin π f s x :=
(starL' π : F βL[π] F).comp_fderivWithin hxs
#align fderiv_within_star fderivWithin_star
+/- warning: fderiv_star -> fderiv_star is a dubious translation:
+lean 3 declaration is
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2)))] {E : Type.{u2}} [_inst_4 : NormedAddCommGroup.{u2} E] [_inst_5 : NormedSpace.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4)] {F : Type.{u3}} [_inst_6 : NormedAddCommGroup.{u3} F] [_inst_7 : StarAddMonoid.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)] [_inst_9 : StarModule.{u1, u3} π F (InvolutiveStar.toHasStar.{u1} π (StarAddMonoid.toHasInvolutiveStar.{u1} π (AddCommMonoid.toAddMonoid.{u1} π (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} π (NonUnitalSemiring.toNonUnitalNonAssocSemiring.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalRing.toNonUnitalSemiring.{u1} π (NonUnitalNormedRing.toNonUnitalRing.{u1} π (NormedRing.toNonUnitalNormedRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) _inst_2))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (SMulZeroClass.toHasSmul.{u1, u3} π F (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π F (MulZeroClass.toHasZero.{u1} π (MulZeroOneClass.toMulZeroClass.{u1} π (MonoidWithZero.toMulZeroOneClass.{u1} π (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π F (Semiring.toMonoidWithZero.{u1} π (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (AddZeroClass.toHasZero.{u3} F (AddMonoid.toAddZeroClass.{u3} F (AddCommMonoid.toAddMonoid.{u3} F (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u3} π F (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} F (SeminormedAddCommGroup.toAddCommGroup.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6))) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u3} F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7))] {f : E -> F} {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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u3} F (InvolutiveStar.toHasStar.{u3} F (StarAddMonoid.toHasInvolutiveStar.{u3} F (SubNegMonoid.toAddMonoid.{u3} F (AddGroup.toSubNegMonoid.{u3} F (NormedAddGroup.toAddGroup.{u3} F (NormedAddCommGroup.toNormedAddGroup.{u3} F _inst_6)))) _inst_7)) (f y)) x) (ContinuousLinearMap.comp.{u1, u1, u1, u2, u3, u3} π 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))))) (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))))))) (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))))))) (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_4)))) (AddCommGroup.toAddCommMonoid.{u2} E (NormedAddCommGroup.toAddCommGroup.{u2} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u2} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} 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)))))))) ((fun (a : Type.{u3}) (b : Type.{u3}) [self : HasLiftT.{succ u3, succ u3} a b] => self.0) (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (HasLiftT.mk.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (CoeTCβ.coe.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (coeBase.{succ u3, succ u3} (ContinuousLinearEquiv.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearMap.{u1, u1, u3, 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))))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8)) (ContinuousLinearEquiv.ContinuousLinearMap.coe.{u1, u1, u3, u3} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (starL'._proof_1.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (starL'._proof_2.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8))))) (starL'.{u1, u3} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u3} F (NormedAddCommGroup.toAddCommGroup.{u3} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u3} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u3} F (PseudoMetricSpace.toUniformSpace.{u3} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} F _inst_6)))) _inst_10)) (fderiv.{u1, u2, u3} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x))
+but is expected to have type
+ forall {π : Type.{u1}} [_inst_1 : NontriviallyNormedField.{u1} π] [_inst_2 : StarRing.{u1} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} π (CommRing.toNonUnitalCommRing.{u1} π (EuclideanDomain.toCommRing.{u1} π (Field.toEuclideanDomain.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))))] [_inst_3 : TrivialStar.{u1} π (InvolutiveStar.toStar.{u1} π (StarAddMonoid.toInvolutiveStar.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (Ring.toAddGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} π (CommRing.toNonUnitalCommRing.{u1} π (EuclideanDomain.toCommRing.{u1} π (Field.toEuclideanDomain.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) _inst_2)))] {E : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} E] [_inst_5 : NormedSpace.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] {F : Type.{u2}} [_inst_6 : NormedAddCommGroup.{u2} F] [_inst_7 : StarAddMonoid.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_6))))] [_inst_8 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)] [_inst_9 : StarModule.{u1, u2} π F (InvolutiveStar.toStar.{u1} π (StarAddMonoid.toInvolutiveStar.{u1} π (AddMonoidWithOne.toAddMonoid.{u1} π (AddGroupWithOne.toAddMonoidWithOne.{u1} π (Ring.toAddGroupWithOne.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (StarRing.toStarAddMonoid.{u1} π (NonUnitalCommSemiring.toNonUnitalSemiring.{u1} π (NonUnitalCommRing.toNonUnitalCommSemiring.{u1} π (CommRing.toNonUnitalCommRing.{u1} π (EuclideanDomain.toCommRing.{u1} π (Field.toEuclideanDomain.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) _inst_2))) (InvolutiveStar.toStar.{u2} F (StarAddMonoid.toInvolutiveStar.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_6)))) _inst_7)) (SMulZeroClass.toSMul.{u1, u2} π F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (CommMonoidWithZero.toZero.{u1} π (CommGroupWithZero.toCommMonoidWithZero.{u1} π (Semifield.toCommGroupWithZero.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π F (Semiring.toMonoidWithZero.{u1} π (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)))))) (Module.toMulActionWithZero.{u1, u2} π F (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8)))))] [_inst_10 : ContinuousStar.{u2} F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (InvolutiveStar.toStar.{u2} F (StarAddMonoid.toInvolutiveStar.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_6)))) _inst_7))] {f : E -> F} {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_4)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 (fun (y : E) => Star.star.{u2} F (InvolutiveStar.toStar.{u2} F (StarAddMonoid.toInvolutiveStar.{u2} F (SubNegMonoid.toAddMonoid.{u2} F (AddGroup.toSubNegMonoid.{u2} F (NormedAddGroup.toAddGroup.{u2} F (NormedAddCommGroup.toNormedAddGroup.{u2} F _inst_6)))) _inst_7)) (f y)) x) (ContinuousLinearMap.comp.{u1, u1, u1, u3, u2, u2} π π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{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_4)))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8) (RingHomCompTriple.ids.{u1, u1} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))))) (ContinuousLinearEquiv.toContinuousLinearMap.{u1, u1, u2, u2} π π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHom.id.{u1} π (Semiring.toNonAssocSemiring.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))))) (RingHomInvPair.ids.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) (RingHomInvPair.ids.{u1} π (CommSemiring.toSemiring.{u1} π (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))))) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8) (starL'.{u1, u2} π F (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) _inst_2 _inst_3 (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_6)) _inst_7 (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6) _inst_8) _inst_9 (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_6)))) _inst_10)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_6 _inst_8 f x))
+Case conversion may be inaccurate. Consider using '#align fderiv_star fderiv_starβ'. -/
@[simp]
theorem fderiv_star :
fderiv π (fun y => star (f y)) x = ((starL' π : F βL[π] F) : F βL[π] F) βL fderiv π f x :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
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)
@@ -25,9 +25,7 @@ star operation; which as should be expected rules out `π = β`.
open scoped Classical
variable {π : Type*} [NontriviallyNormedField π] [StarRing π] [TrivialStar π]
-
variable {E : Type*} [NormedAddCommGroup E] [NormedSpace π E]
-
variable {F : Type*} [NormedAddCommGroup F] [StarAddMonoid F] [NormedSpace π F] [StarModule π F]
[ContinuousStar F]
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.
@@ -33,6 +33,7 @@ variable {F : Type*} [NormedAddCommGroup F] [StarAddMonoid F] [NormedSpace π
variable {f : E β F} {f' : E βL[π] F} (e : E βL[π] F) {x : E} {s : Set E} {L : Filter E}
+@[fun_prop]
theorem HasStrictFDerivAt.star (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x :=
(starL' π : F βL[π] F).toContinuousLinearMap.hasStrictFDerivAt.comp x h
@@ -43,16 +44,19 @@ theorem HasFDerivAtFilter.star (h : HasFDerivAtFilter f f' x L) :
(starL' π : F βL[π] F).toContinuousLinearMap.hasFDerivAtFilter.comp x h Filter.tendsto_map
#align has_fderiv_at_filter.star HasFDerivAtFilter.star
+@[fun_prop]
nonrec theorem HasFDerivWithinAt.star (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') s x :=
h.star
#align has_fderiv_within_at.star HasFDerivWithinAt.star
+@[fun_prop]
nonrec theorem HasFDerivAt.star (h : HasFDerivAt f f' x) :
HasFDerivAt (fun x => star (f x)) (((starL' π : F βL[π] F) : F βL[π] F) βL f') x :=
h.star
#align has_fderiv_at.star HasFDerivAt.star
+@[fun_prop]
theorem DifferentiableWithinAt.star (h : DifferentiableWithinAt π f s x) :
DifferentiableWithinAt π (fun y => star (f y)) s x :=
h.hasFDerivWithinAt.star.differentiableWithinAt
@@ -64,6 +68,7 @@ theorem differentiableWithinAt_star_iff :
(starL' π : F βL[π] F).comp_differentiableWithinAt_iff
#align differentiable_within_at_star_iff differentiableWithinAt_star_iff
+@[fun_prop]
theorem DifferentiableAt.star (h : DifferentiableAt π f x) :
DifferentiableAt π (fun y => star (f y)) x :=
h.hasFDerivAt.star.differentiableAt
@@ -75,6 +80,7 @@ theorem differentiableAt_star_iff :
(starL' π : F βL[π] F).comp_differentiableAt_iff
#align differentiable_at_star_iff differentiableAt_star_iff
+@[fun_prop]
theorem DifferentiableOn.star (h : DifferentiableOn π f s) :
DifferentiableOn π (fun y => star (f y)) s := fun x hx => (h x hx).star
#align differentiable_on.star DifferentiableOn.star
@@ -85,6 +91,7 @@ theorem differentiableOn_star_iff :
(starL' π : F βL[π] F).comp_differentiableOn_iff
#align differentiable_on_star_iff differentiableOn_star_iff
+@[fun_prop]
theorem Differentiable.star (h : Differentiable π f) : Differentiable π fun y => star (f y) :=
fun x => (h x).star
#align differentiable.star Differentiable.star
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.
@@ -22,7 +22,7 @@ star operation; which as should be expected rules out `π = β`.
-/
-open Classical
+open scoped Classical
variable {π : Type*} [NontriviallyNormedField π] [StarRing π] [TrivialStar π]
@@ -6,7 +6,7 @@ Authors: Eric Wieser
import Mathlib.Analysis.Calculus.FDeriv.Linear
import Mathlib.Analysis.Calculus.FDeriv.Comp
import Mathlib.Analysis.Calculus.FDeriv.Equiv
-import Mathlib.Analysis.NormedSpace.Star.Basic
+import Mathlib.Topology.Algebra.Module.Star
#align_import analysis.calculus.fderiv.star from "leanprover-community/mathlib"@"ad84a13c884fd19e286fb7abb36f4b9ba7e2f615"
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -24,11 +24,11 @@ star operation; which as should be expected rules out `π = β`.
open Classical
-variable {π : Type _} [NontriviallyNormedField π] [StarRing π] [TrivialStar π]
+variable {π : Type*} [NontriviallyNormedField π] [StarRing π] [TrivialStar π]
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace π E]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace π E]
-variable {F : Type _} [NormedAddCommGroup F] [StarAddMonoid F] [NormedSpace π F] [StarModule π F]
+variable {F : Type*} [NormedAddCommGroup F] [StarAddMonoid F] [NormedSpace π F] [StarModule π F]
[ContinuousStar F]
variable {f : E β F} {f' : E βL[π] F} (e : E βL[π] F) {x : E} {s : Set E} {L : Filter E}
@@ -2,17 +2,14 @@
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module analysis.calculus.fderiv.star
-! leanprover-community/mathlib commit ad84a13c884fd19e286fb7abb36f4b9ba7e2f615
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Analysis.Calculus.FDeriv.Linear
import Mathlib.Analysis.Calculus.FDeriv.Comp
import Mathlib.Analysis.Calculus.FDeriv.Equiv
import Mathlib.Analysis.NormedSpace.Star.Basic
+#align_import analysis.calculus.fderiv.star from "leanprover-community/mathlib"@"ad84a13c884fd19e286fb7abb36f4b9ba7e2f615"
+
/-!
# Star operations on derivatives
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