analysis.calculus.fderiv.restrict_scalars
β·
Mathlib.Analysis.Calculus.FDeriv.RestrictScalars
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
-/
-import Analysis.Calculus.Fderiv.Basic
+import Analysis.Calculus.FDeriv.Basic
#align_import analysis.calculus.fderiv.restrict_scalars from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -107,13 +107,13 @@ theorem Differentiable.restrictScalars (h : Differentiable π' f) : Differenti
#print HasFDerivWithinAt.of_restrictScalars /-
theorem HasFDerivWithinAt.of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
- (H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x := by rw [β H] at h ; exact h
+ (H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x := by rw [β H] at h; exact h
#align has_fderiv_within_at_of_restrict_scalars HasFDerivWithinAt.of_restrictScalars
-/
#print hasFDerivAt_of_restrictScalars /-
theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f g' x)
- (H : f'.restrictScalars π = g') : HasFDerivAt f f' x := by rw [β H] at h ; exact h
+ (H : f'.restrictScalars π = g') : HasFDerivAt f f' x := by rw [β H] at h; exact h
#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalars
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -105,10 +105,10 @@ theorem Differentiable.restrictScalars (h : Differentiable π' f) : Differenti
#align differentiable.restrict_scalars Differentiable.restrictScalars
-/
-#print hasFDerivWithinAt_of_restrictScalars /-
-theorem hasFDerivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
+#print HasFDerivWithinAt.of_restrictScalars /-
+theorem HasFDerivWithinAt.of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
(H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x := by rw [β H] at h ; exact h
-#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalars
+#align has_fderiv_within_at_of_restrict_scalars HasFDerivWithinAt.of_restrictScalars
-/
#print hasFDerivAt_of_restrictScalars /-
@@ -134,7 +134,7 @@ theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt
Β· rintro β¨g', hg'β©
exact β¨g', hs.eq (hg'.restrict_scalars π) hf.has_fderiv_within_atβ©
Β· rintro β¨f', hf'β©
- exact β¨f', hasFDerivWithinAt_of_restrictScalars π hf.has_fderiv_within_at hf'β©
+ exact β¨f', HasFDerivWithinAt.of_restrictScalars π hf.has_fderiv_within_at hf'β©
#align differentiable_within_at_iff_restrict_scalars differentiableWithinAt_iff_restrictScalars
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
-/
-import Mathbin.Analysis.Calculus.Fderiv.Basic
+import Analysis.Calculus.Fderiv.Basic
#align_import analysis.calculus.fderiv.restrict_scalars from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.calculus.fderiv.restrict_scalars
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Analysis.Calculus.Fderiv.Basic
+#align_import analysis.calculus.fderiv.restrict_scalars from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
/-!
# The derivative of the scalar restriction of a linear map
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -55,56 +55,79 @@ variable [IsScalarTower π π' F]
variable {f : E β F} {f' : E βL[π'] F} {s : Set E} {x : E}
+#print HasStrictFDerivAt.restrictScalars /-
theorem HasStrictFDerivAt.restrictScalars (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt f (f'.restrictScalars π) x :=
h
#align has_strict_fderiv_at.restrict_scalars HasStrictFDerivAt.restrictScalars
+-/
+#print HasFDerivAtFilter.restrictScalars /-
theorem HasFDerivAtFilter.restrictScalars {L} (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter f (f'.restrictScalars π) x L :=
h
#align has_fderiv_at_filter.restrict_scalars HasFDerivAtFilter.restrictScalars
+-/
+#print HasFDerivAt.restrictScalars /-
theorem HasFDerivAt.restrictScalars (h : HasFDerivAt f f' x) :
HasFDerivAt f (f'.restrictScalars π) x :=
h
#align has_fderiv_at.restrict_scalars HasFDerivAt.restrictScalars
+-/
+#print HasFDerivWithinAt.restrictScalars /-
theorem HasFDerivWithinAt.restrictScalars (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt f (f'.restrictScalars π) s x :=
h
#align has_fderiv_within_at.restrict_scalars HasFDerivWithinAt.restrictScalars
+-/
+#print DifferentiableAt.restrictScalars /-
theorem DifferentiableAt.restrictScalars (h : DifferentiableAt π' f x) : DifferentiableAt π f x :=
(h.HasFDerivAt.restrictScalars π).DifferentiableAt
#align differentiable_at.restrict_scalars DifferentiableAt.restrictScalars
+-/
+#print DifferentiableWithinAt.restrictScalars /-
theorem DifferentiableWithinAt.restrictScalars (h : DifferentiableWithinAt π' f s x) :
DifferentiableWithinAt π f s x :=
(h.HasFDerivWithinAt.restrictScalars π).DifferentiableWithinAt
#align differentiable_within_at.restrict_scalars DifferentiableWithinAt.restrictScalars
+-/
+#print DifferentiableOn.restrictScalars /-
theorem DifferentiableOn.restrictScalars (h : DifferentiableOn π' f s) : DifferentiableOn π f s :=
fun x hx => (h x hx).restrictScalars π
#align differentiable_on.restrict_scalars DifferentiableOn.restrictScalars
+-/
+#print Differentiable.restrictScalars /-
theorem Differentiable.restrictScalars (h : Differentiable π' f) : Differentiable π f := fun x =>
(h x).restrictScalars π
#align differentiable.restrict_scalars Differentiable.restrictScalars
+-/
+#print hasFDerivWithinAt_of_restrictScalars /-
theorem hasFDerivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
(H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x := by rw [β H] at h ; exact h
#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalars
+-/
+#print hasFDerivAt_of_restrictScalars /-
theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f g' x)
(H : f'.restrictScalars π = g') : HasFDerivAt f f' x := by rw [β H] at h ; exact h
#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalars
+-/
+#print DifferentiableAt.fderiv_restrictScalars /-
theorem DifferentiableAt.fderiv_restrictScalars (h : DifferentiableAt π' f x) :
fderiv π f x = (fderiv π' f x).restrictScalars π :=
(h.HasFDerivAt.restrictScalars π).fderiv
#align differentiable_at.fderiv_restrict_scalars DifferentiableAt.fderiv_restrictScalars
+-/
+#print differentiableWithinAt_iff_restrictScalars /-
theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt π f s x)
(hs : UniqueDiffWithinAt π s x) :
DifferentiableWithinAt π' f s x β
@@ -116,7 +139,9 @@ theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt
Β· rintro β¨f', hf'β©
exact β¨f', hasFDerivWithinAt_of_restrictScalars π hf.has_fderiv_within_at hf'β©
#align differentiable_within_at_iff_restrict_scalars differentiableWithinAt_iff_restrictScalars
+-/
+#print differentiableAt_iff_restrictScalars /-
theorem differentiableAt_iff_restrictScalars (hf : DifferentiableAt π f x) :
DifferentiableAt π' f x β β g' : E βL[π'] F, g'.restrictScalars π = fderiv π f x :=
by
@@ -124,6 +149,7 @@ theorem differentiableAt_iff_restrictScalars (hf : DifferentiableAt π f x) :
exact
differentiableWithinAt_iff_restrictScalars π hf.differentiable_within_at uniqueDiffWithinAt_univ
#align differentiable_at_iff_restrict_scalars differentiableAt_iff_restrictScalars
+-/
end RestrictScalars
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -93,11 +93,11 @@ theorem Differentiable.restrictScalars (h : Differentiable π' f) : Differenti
#align differentiable.restrict_scalars Differentiable.restrictScalars
theorem hasFDerivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
- (H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x := by rw [β H] at h; exact h
+ (H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x := by rw [β H] at h ; exact h
#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalars
theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f g' x)
- (H : f'.restrictScalars π = g') : HasFDerivAt f f' x := by rw [β H] at h; exact h
+ (H : f'.restrictScalars π = g') : HasFDerivAt f f' x := by rw [β H] at h ; exact h
#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalars
theorem DifferentiableAt.fderiv_restrictScalars (h : DifferentiableAt π' f x) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -26,7 +26,7 @@ the scalar restriction of a linear map.
open Filter Asymptotics ContinuousLinearMap Set Metric
-open Topology Classical NNReal Filter Asymptotics ENNReal
+open scoped Topology Classical NNReal Filter Asymptotics ENNReal
noncomputable section
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -55,92 +55,56 @@ variable [IsScalarTower π π' F]
variable {f : E β F} {f' : E βL[π'] F} {s : Set E} {x : E}
-/- warning: has_strict_fderiv_at.restrict_scalars -> HasStrictFDerivAt.restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.restrict_scalars HasStrictFDerivAt.restrictScalarsβ'. -/
theorem HasStrictFDerivAt.restrictScalars (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt f (f'.restrictScalars π) x :=
h
#align has_strict_fderiv_at.restrict_scalars HasStrictFDerivAt.restrictScalars
-/- warning: has_fderiv_at_filter.restrict_scalars -> HasFDerivAtFilter.restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.restrict_scalars HasFDerivAtFilter.restrictScalarsβ'. -/
theorem HasFDerivAtFilter.restrictScalars {L} (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter f (f'.restrictScalars π) x L :=
h
#align has_fderiv_at_filter.restrict_scalars HasFDerivAtFilter.restrictScalars
-/- warning: has_fderiv_at.restrict_scalars -> HasFDerivAt.restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at.restrict_scalars HasFDerivAt.restrictScalarsβ'. -/
theorem HasFDerivAt.restrictScalars (h : HasFDerivAt f f' x) :
HasFDerivAt f (f'.restrictScalars π) x :=
h
#align has_fderiv_at.restrict_scalars HasFDerivAt.restrictScalars
-/- warning: has_fderiv_within_at.restrict_scalars -> HasFDerivWithinAt.restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.restrict_scalars HasFDerivWithinAt.restrictScalarsβ'. -/
theorem HasFDerivWithinAt.restrictScalars (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt f (f'.restrictScalars π) s x :=
h
#align has_fderiv_within_at.restrict_scalars HasFDerivWithinAt.restrictScalars
-/- warning: differentiable_at.restrict_scalars -> DifferentiableAt.restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_at.restrict_scalars DifferentiableAt.restrictScalarsβ'. -/
theorem DifferentiableAt.restrictScalars (h : DifferentiableAt π' f x) : DifferentiableAt π f x :=
(h.HasFDerivAt.restrictScalars π).DifferentiableAt
#align differentiable_at.restrict_scalars DifferentiableAt.restrictScalars
-/- warning: differentiable_within_at.restrict_scalars -> DifferentiableWithinAt.restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_within_at.restrict_scalars DifferentiableWithinAt.restrictScalarsβ'. -/
theorem DifferentiableWithinAt.restrictScalars (h : DifferentiableWithinAt π' f s x) :
DifferentiableWithinAt π f s x :=
(h.HasFDerivWithinAt.restrictScalars π).DifferentiableWithinAt
#align differentiable_within_at.restrict_scalars DifferentiableWithinAt.restrictScalars
-/- warning: differentiable_on.restrict_scalars -> DifferentiableOn.restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_on.restrict_scalars DifferentiableOn.restrictScalarsβ'. -/
theorem DifferentiableOn.restrictScalars (h : DifferentiableOn π' f s) : DifferentiableOn π f s :=
fun x hx => (h x hx).restrictScalars π
#align differentiable_on.restrict_scalars DifferentiableOn.restrictScalars
-/- warning: differentiable.restrict_scalars -> Differentiable.restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable.restrict_scalars Differentiable.restrictScalarsβ'. -/
theorem Differentiable.restrictScalars (h : Differentiable π' f) : Differentiable π f := fun x =>
(h x).restrictScalars π
#align differentiable.restrict_scalars Differentiable.restrictScalars
-/- warning: has_fderiv_within_at_of_restrict_scalars -> hasFDerivWithinAt_of_restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalarsβ'. -/
theorem hasFDerivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
(H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x := by rw [β H] at h; exact h
#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalars
-/- warning: has_fderiv_at_of_restrict_scalars -> hasFDerivAt_of_restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalarsβ'. -/
theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f g' x)
(H : f'.restrictScalars π = g') : HasFDerivAt f f' x := by rw [β H] at h; exact h
#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalars
-/- warning: differentiable_at.fderiv_restrict_scalars -> DifferentiableAt.fderiv_restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_at.fderiv_restrict_scalars DifferentiableAt.fderiv_restrictScalarsβ'. -/
theorem DifferentiableAt.fderiv_restrictScalars (h : DifferentiableAt π' f x) :
fderiv π f x = (fderiv π' f x).restrictScalars π :=
(h.HasFDerivAt.restrictScalars π).fderiv
#align differentiable_at.fderiv_restrict_scalars DifferentiableAt.fderiv_restrictScalars
-/- warning: differentiable_within_at_iff_restrict_scalars -> differentiableWithinAt_iff_restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_within_at_iff_restrict_scalars differentiableWithinAt_iff_restrictScalarsβ'. -/
theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt π f s x)
(hs : UniqueDiffWithinAt π s x) :
DifferentiableWithinAt π' f s x β
@@ -153,9 +117,6 @@ theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt
exact β¨f', hasFDerivWithinAt_of_restrictScalars π hf.has_fderiv_within_at hf'β©
#align differentiable_within_at_iff_restrict_scalars differentiableWithinAt_iff_restrictScalars
-/- warning: differentiable_at_iff_restrict_scalars -> differentiableAt_iff_restrictScalars is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align differentiable_at_iff_restrict_scalars differentiableAt_iff_restrictScalarsβ'. -/
theorem differentiableAt_iff_restrictScalars (hf : DifferentiableAt π f x) :
DifferentiableAt π' f x β β g' : E βL[π'] F, g'.restrictScalars π = fderiv π f x :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -120,20 +120,14 @@ theorem Differentiable.restrictScalars (h : Differentiable π' f) : Differenti
<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalarsβ'. -/
theorem hasFDerivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
- (H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x :=
- by
- rw [β H] at h
- exact h
+ (H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x := by rw [β H] at h; exact h
#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalars
/- warning: has_fderiv_at_of_restrict_scalars -> hasFDerivAt_of_restrictScalars is a dubious translation:
<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalarsβ'. -/
theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f g' x)
- (H : f'.restrictScalars π = g') : HasFDerivAt f f' x :=
- by
- rw [β H] at h
- exact h
+ (H : f'.restrictScalars π = g') : HasFDerivAt f f' x := by rw [β H] at h; exact h
#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalars
/- warning: differentiable_at.fderiv_restrict_scalars -> DifferentiableAt.fderiv_restrictScalars is a dubious translation:
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -56,10 +56,7 @@ variable [IsScalarTower π π' F]
variable {f : E β F} {f' : E βL[π'] F} {s : Set E} {x : E}
/- warning: has_strict_fderiv_at.restrict_scalars -> HasStrictFDerivAt.restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {x : E}, (HasStrictFDerivAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x) -> (HasStrictFDerivAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') x)
-but is expected to have type
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u4, u4, u3, u2} π' π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (RingHom.id.{u4} π' (Semiring.toNonAssocSemiring.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {x : E}, (HasStrictFDerivAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x) -> (HasStrictFDerivAt.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} π' E F (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (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_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u1, u4} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u4} π' (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _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 (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 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)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} 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.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.restrict_scalars HasStrictFDerivAt.restrictScalarsβ'. -/
theorem HasStrictFDerivAt.restrictScalars (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt f (f'.restrictScalars π) x :=
@@ -67,10 +64,7 @@ theorem HasStrictFDerivAt.restrictScalars (h : HasStrictFDerivAt f f' x) :
#align has_strict_fderiv_at.restrict_scalars HasStrictFDerivAt.restrictScalars
/- warning: has_fderiv_at_filter.restrict_scalars -> HasFDerivAtFilter.restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {x : E} {L : Filter.{u3} E}, (HasFDerivAtFilter.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x L) -> (HasFDerivAtFilter.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') x L)
-but is expected to have type
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u3}} [_inst_2 : NontriviallyNormedField.{u3} π'] [_inst_3 : NormedAlgebra.{u1, u3} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u3} π' (NormedCommRing.toSeminormedCommRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))] {E : Type.{u4}} [_inst_4 : NormedAddCommGroup.{u4} E] [_inst_5 : NormedSpace.{u1, u4} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4)] [_inst_6 : NormedSpace.{u3, u4} π' E (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u3, u4} π π' E (Algebra.toSMul.{u1, u3} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u3} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u3} π' (NormedCommRing.toSeminormedCommRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u3, u4} π' E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u3, u4} π' E (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_2)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u3, u4} π' E (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_2)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (Module.toMulActionWithZero.{u3, u4} π' E (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)) (NormedSpace.toModule.{u3, u4} π' E (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u4} π E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u4} π E (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.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} π E (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.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)) (NormedSpace.toModule.{u1, u4} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u3, u2} π' F (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u3, u2} π π' F (Algebra.toSMul.{u1, u3} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u3} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u3} π' (NormedCommRing.toSeminormedCommRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u3, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 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_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 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_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u3, u2} π' F (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u3, u2} π' F (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u4, u2} π' π' (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (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_2))))))) E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u3, u4} π' E (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_6) (NormedSpace.toModule.{u3, u2} π' F (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {x : E} {L : Filter.{u4} E}, (HasFDerivAtFilter.{u3, u4, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x L) -> (HasFDerivAtFilter.{u1, u4, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u3, u4, u2, u1} π' E F (NormedRing.toRing.{u3} π' (NormedCommRing.toNormedRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u3, u4} π' E (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_6) (NormedSpace.toModule.{u3, u2} π' F (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u4} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u4, u2, u1, u3} E F (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u3} π' (NormedRing.toRing.{u3} π' (NormedCommRing.toNormedRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (Algebra.toSMul.{u1, u3} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u3} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u3} π' (NormedCommRing.toSeminormedCommRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u4} π E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u1, u4} π E (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} π E (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)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4))))))) (Module.toMulActionWithZero.{u1, u4} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4))) (NormedSpace.toModule.{u1, u4} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u3, u4} π' E (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _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 (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 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)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} 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.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u3, u2} π' F (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') x L)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.restrict_scalars HasFDerivAtFilter.restrictScalarsβ'. -/
theorem HasFDerivAtFilter.restrictScalars {L} (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter f (f'.restrictScalars π) x L :=
@@ -78,10 +72,7 @@ theorem HasFDerivAtFilter.restrictScalars {L} (h : HasFDerivAtFilter f f' x L) :
#align has_fderiv_at_filter.restrict_scalars HasFDerivAtFilter.restrictScalars
/- warning: has_fderiv_at.restrict_scalars -> HasFDerivAt.restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {x : E}, (HasFDerivAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x) -> (HasFDerivAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') x)
-but is expected to have type
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u4, u4, u3, u2} π' π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (RingHom.id.{u4} π' (Semiring.toNonAssocSemiring.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {x : E}, (HasFDerivAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x) -> (HasFDerivAt.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} π' E F (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (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_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u1, u4} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u4} π' (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _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 (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 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)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} 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.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at.restrict_scalars HasFDerivAt.restrictScalarsβ'. -/
theorem HasFDerivAt.restrictScalars (h : HasFDerivAt f f' x) :
HasFDerivAt f (f'.restrictScalars π) x :=
@@ -89,10 +80,7 @@ theorem HasFDerivAt.restrictScalars (h : HasFDerivAt f f' x) :
#align has_fderiv_at.restrict_scalars HasFDerivAt.restrictScalars
/- warning: has_fderiv_within_at.restrict_scalars -> HasFDerivWithinAt.restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {s : Set.{u3} E} {x : E}, (HasFDerivWithinAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' s x) -> (HasFDerivWithinAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') s x)
-but is expected to have type
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u4, u4, u3, u2} π' π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (RingHom.id.{u4} π' (Semiring.toNonAssocSemiring.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {s : Set.{u3} E} {x : E}, (HasFDerivWithinAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' s x) -> (HasFDerivWithinAt.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} π' E F (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (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_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u1, u4} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u4} π' (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _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 (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 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)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} 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.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.restrict_scalars HasFDerivWithinAt.restrictScalarsβ'. -/
theorem HasFDerivWithinAt.restrictScalars (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt f (f'.restrictScalars π) s x :=
@@ -100,20 +88,14 @@ theorem HasFDerivWithinAt.restrictScalars (h : HasFDerivWithinAt f f' s x) :
#align has_fderiv_within_at.restrict_scalars HasFDerivWithinAt.restrictScalars
/- warning: differentiable_at.restrict_scalars -> DifferentiableAt.restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) -> (DifferentiableAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x)
-but is expected to have type
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) -> (DifferentiableAt.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_at.restrict_scalars DifferentiableAt.restrictScalarsβ'. -/
theorem DifferentiableAt.restrictScalars (h : DifferentiableAt π' f x) : DifferentiableAt π f x :=
(h.HasFDerivAt.restrictScalars π).DifferentiableAt
#align differentiable_at.restrict_scalars DifferentiableAt.restrictScalars
/- warning: differentiable_within_at.restrict_scalars -> DifferentiableWithinAt.restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E} {x : E}, (DifferentiableWithinAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s x) -> (DifferentiableWithinAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x)
-but is expected to have type
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E} {x : E}, (DifferentiableWithinAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s x) -> (DifferentiableWithinAt.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_within_at.restrict_scalars DifferentiableWithinAt.restrictScalarsβ'. -/
theorem DifferentiableWithinAt.restrictScalars (h : DifferentiableWithinAt π' f s x) :
DifferentiableWithinAt π f s x :=
@@ -121,30 +103,21 @@ theorem DifferentiableWithinAt.restrictScalars (h : DifferentiableWithinAt π'
#align differentiable_within_at.restrict_scalars DifferentiableWithinAt.restrictScalars
/- warning: differentiable_on.restrict_scalars -> DifferentiableOn.restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E}, (DifferentiableOn.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s) -> (DifferentiableOn.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s)
-but is expected to have type
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E}, (DifferentiableOn.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s) -> (DifferentiableOn.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_on.restrict_scalars DifferentiableOn.restrictScalarsβ'. -/
theorem DifferentiableOn.restrictScalars (h : DifferentiableOn π' f s) : DifferentiableOn π f s :=
fun x hx => (h x hx).restrictScalars π
#align differentiable_on.restrict_scalars DifferentiableOn.restrictScalars
/- warning: differentiable.restrict_scalars -> Differentiable.restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F}, (Differentiable.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f) -> (Differentiable.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f)
-but is expected to have type
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F}, (Differentiable.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f) -> (Differentiable.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f)
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable.restrict_scalars Differentiable.restrictScalarsβ'. -/
theorem Differentiable.restrictScalars (h : Differentiable π' f) : Differentiable π f := fun x =>
(h x).restrictScalars π
#align differentiable.restrict_scalars Differentiable.restrictScalars
/- warning: has_fderiv_within_at_of_restrict_scalars -> hasFDerivWithinAt_of_restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {s : Set.{u3} E} {x : E} {g' : ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)}, (HasFDerivWithinAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f g' s x) -> (Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') g') -> (HasFDerivWithinAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' s x)
-but is expected to have type
- forall (π : Type.{u4}) [_inst_1 : NontriviallyNormedField.{u4} π] {π' : Type.{u1}} [_inst_2 : NontriviallyNormedField.{u1} π'] [_inst_3 : NormedAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))] {E : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} E] [_inst_5 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_6 : NormedSpace.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u4, u1, u3} π π' E (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π' E (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π E (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u4, u1, u2} π π' F (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (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_8)))))) (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_2)))))) (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_8)))))) (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_2)))))) (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_8)))))) (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_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (Module.toMulActionWithZero.{u4, u2} π F (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : 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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {s : Set.{u3} E} {x : E} {g' : ContinuousLinearMap.{u4, u4, u3, u2} π π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)}, (HasFDerivWithinAt.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f g' s x) -> (Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u4, u4, u3, u2} π π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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 (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u1, u3, u2, u4} π' E F (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u4, u1} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u1} π' (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u4, u3} π E (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toSMul.{u4, u2} π F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u4, u2} π F (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') g') -> (HasFDerivWithinAt.{u1, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' s x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalarsβ'. -/
theorem hasFDerivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
(H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x :=
@@ -154,10 +127,7 @@ theorem hasFDerivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDeri
#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalars
/- warning: has_fderiv_at_of_restrict_scalars -> hasFDerivAt_of_restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {x : E} {g' : ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)}, (HasFDerivAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f g' x) -> (Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') g') -> (HasFDerivAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x)
-but is expected to have type
- forall (π : Type.{u4}) [_inst_1 : NontriviallyNormedField.{u4} π] {π' : Type.{u1}} [_inst_2 : NontriviallyNormedField.{u1} π'] [_inst_3 : NormedAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))] {E : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} E] [_inst_5 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_6 : NormedSpace.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u4, u1, u3} π π' E (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π' E (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π E (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u4, u1, u2} π π' F (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (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_8)))))) (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_2)))))) (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_8)))))) (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_2)))))) (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_8)))))) (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_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (Module.toMulActionWithZero.{u4, u2} π F (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : 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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {x : E} {g' : ContinuousLinearMap.{u4, u4, u3, u2} π π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)}, (HasFDerivAt.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f g' x) -> (Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u4, u4, u3, u2} π π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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 (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u1, u3, u2, u4} π' E F (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u4, u1} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u1} π' (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u4, u3} π E (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toSMul.{u4, u2} π F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u4, u2} π F (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') g') -> (HasFDerivAt.{u1, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x)
+<too large>
Case conversion may be inaccurate. Consider using '#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalarsβ'. -/
theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f g' x)
(H : f'.restrictScalars π = g') : HasFDerivAt f f' x :=
@@ -167,10 +137,7 @@ theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f
#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalars
/- warning: differentiable_at.fderiv_restrict_scalars -> DifferentiableAt.fderiv_restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) -> (Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)) (fderiv.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x) (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) (fderiv.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x)))
-but is expected to have type
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) -> (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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (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_8) _inst_9)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} π' E F (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (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_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u1, u4} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u4} π' (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _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 (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 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)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} 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.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) (fderiv.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x)))
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_at.fderiv_restrict_scalars DifferentiableAt.fderiv_restrictScalarsβ'. -/
theorem DifferentiableAt.fderiv_restrictScalars (h : DifferentiableAt π' f x) :
fderiv π f x = (fderiv π' f x).restrictScalars π :=
@@ -178,10 +145,7 @@ theorem DifferentiableAt.fderiv_restrictScalars (h : DifferentiableAt π' f x)
#align differentiable_at.fderiv_restrict_scalars DifferentiableAt.fderiv_restrictScalars
/- warning: differentiable_within_at_iff_restrict_scalars -> differentiableWithinAt_iff_restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E} {x : E}, (DifferentiableWithinAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x) -> (UniqueDiffWithinAt.{u1, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) s x) -> (Iff (DifferentiableWithinAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s x) (Exists.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)) (fun (g' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)) => Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) g') (fderivWithin.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x))))
-but is expected to have type
- forall (π : Type.{u4}) [_inst_1 : NontriviallyNormedField.{u4} π] {π' : Type.{u1}} [_inst_2 : NontriviallyNormedField.{u1} π'] [_inst_3 : NormedAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))] {E : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} E] [_inst_5 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_6 : NormedSpace.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u4, u1, u3} π π' E (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π' E (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π E (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u4, u1, u2} π π' F (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (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_8)))))) (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_2)))))) (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_8)))))) (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_2)))))) (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_8)))))) (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_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (Module.toMulActionWithZero.{u4, u2} π F (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E} {x : E}, (DifferentiableWithinAt.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x) -> (UniqueDiffWithinAt.{u4, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) s x) -> (Iff (DifferentiableWithinAt.{u1, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s x) (Exists.{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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)) (fun (g' : 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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)) => Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u4, u4, u3, u2} π π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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 (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u1, u3, u2, u4} π' E F (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u4, u1} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u1} π' (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u4, u3} π E (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toSMul.{u4, u2} π F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u4, u2} π F (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) g') (fderivWithin.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x))))
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_within_at_iff_restrict_scalars differentiableWithinAt_iff_restrictScalarsβ'. -/
theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt π f s x)
(hs : UniqueDiffWithinAt π s x) :
@@ -196,10 +160,7 @@ theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt
#align differentiable_within_at_iff_restrict_scalars differentiableWithinAt_iff_restrictScalars
/- warning: differentiable_at_iff_restrict_scalars -> differentiableAt_iff_restrictScalars is a dubious translation:
-lean 3 declaration is
- forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x) -> (Iff (DifferentiableAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) (Exists.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)) (fun (g' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)) => Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) g') (fderiv.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x))))
-but is expected to have type
- forall (π : Type.{u4}) [_inst_1 : NontriviallyNormedField.{u4} π] {π' : Type.{u1}} [_inst_2 : NontriviallyNormedField.{u1} π'] [_inst_3 : NormedAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))] {E : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} E] [_inst_5 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_6 : NormedSpace.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u4, u1, u3} π π' E (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π' E (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π E (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u4, u1, u2} π π' F (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (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_8)))))) (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_2)))))) (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_8)))))) (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_2)))))) (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_8)))))) (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_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (Module.toMulActionWithZero.{u4, u2} π F (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x) -> (Iff (DifferentiableAt.{u1, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) (Exists.{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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)) (fun (g' : 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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)) => Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u4, u4, u3, u2} π π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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 (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u1, u3, u2, u4} π' E F (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u4, u1} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u1} π' (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u4, u3} π E (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toSMul.{u4, u2} π F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u4, u2} π F (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) g') (fderiv.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x))))
+<too large>
Case conversion may be inaccurate. Consider using '#align differentiable_at_iff_restrict_scalars differentiableAt_iff_restrictScalarsβ'. -/
theorem differentiableAt_iff_restrictScalars (hf : DifferentiableAt π f x) :
DifferentiableAt π' f x β β g' : E βL[π'] F, g'.restrictScalars π = fderiv π f x :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
! This file was ported from Lean 3 source module analysis.calculus.fderiv.restrict_scalars
-! leanprover-community/mathlib commit e3fb84046afd187b710170887195d50bada934ee
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.Calculus.Fderiv.Basic
/-!
# The derivative of the scalar restriction of a linear map
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
For detailed documentation of the FrΓ©chet derivative,
see the module docstring of `analysis/calculus/fderiv/basic.lean`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -52,43 +52,97 @@ variable [IsScalarTower π π' F]
variable {f : E β F} {f' : E βL[π'] F} {s : Set E} {x : E}
+/- warning: has_strict_fderiv_at.restrict_scalars -> HasStrictFDerivAt.restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {x : E}, (HasStrictFDerivAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x) -> (HasStrictFDerivAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') x)
+but is expected to have type
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u4, u4, u3, u2} π' π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (RingHom.id.{u4} π' (Semiring.toNonAssocSemiring.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {x : E}, (HasStrictFDerivAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x) -> (HasStrictFDerivAt.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} π' E F (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (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_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u1, u4} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u4} π' (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _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 (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 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)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} 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.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') x)
+Case conversion may be inaccurate. Consider using '#align has_strict_fderiv_at.restrict_scalars HasStrictFDerivAt.restrictScalarsβ'. -/
theorem HasStrictFDerivAt.restrictScalars (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt f (f'.restrictScalars π) x :=
h
#align has_strict_fderiv_at.restrict_scalars HasStrictFDerivAt.restrictScalars
+/- warning: has_fderiv_at_filter.restrict_scalars -> HasFDerivAtFilter.restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {x : E} {L : Filter.{u3} E}, (HasFDerivAtFilter.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x L) -> (HasFDerivAtFilter.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') x L)
+but is expected to have type
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u3}} [_inst_2 : NontriviallyNormedField.{u3} π'] [_inst_3 : NormedAlgebra.{u1, u3} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u3} π' (NormedCommRing.toSeminormedCommRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))] {E : Type.{u4}} [_inst_4 : NormedAddCommGroup.{u4} E] [_inst_5 : NormedSpace.{u1, u4} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4)] [_inst_6 : NormedSpace.{u3, u4} π' E (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u3, u4} π π' E (Algebra.toSMul.{u1, u3} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u3} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u3} π' (NormedCommRing.toSeminormedCommRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u3, u4} π' E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u3, u4} π' E (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_2)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u3, u4} π' E (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_2)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (Module.toMulActionWithZero.{u3, u4} π' E (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)) (NormedSpace.toModule.{u3, u4} π' E (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u4} π E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u4} π E (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.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} π E (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.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u4} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)) (NormedSpace.toModule.{u1, u4} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u3, u2} π' F (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u3, u2} π π' F (Algebra.toSMul.{u1, u3} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u3} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u3} π' (NormedCommRing.toSeminormedCommRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u3, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u3, u2} 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_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u3, u2} 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_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u3, u2} π' F (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u3, u2} π' F (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u3, u3, u4, u2} π' π' (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (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_2))))))) E (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4)))) (AddCommGroup.toAddCommMonoid.{u4} E (NormedAddCommGroup.toAddCommGroup.{u4} E _inst_4)) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u3, u4} π' E (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_6) (NormedSpace.toModule.{u3, u2} π' F (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {x : E} {L : Filter.{u4} E}, (HasFDerivAtFilter.{u3, u4, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x L) -> (HasFDerivAtFilter.{u1, u4, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u3, u4, u2, u1} π' E F (NormedRing.toRing.{u3} π' (NormedCommRing.toNormedRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u3, u4} π' E (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_6) (NormedSpace.toModule.{u3, u2} π' F (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u4} E (PseudoMetricSpace.toUniformSpace.{u4} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u4} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u4, u2, u1, u3} E F (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u3} π' (NormedRing.toRing.{u3} π' (NormedCommRing.toNormedRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (Algebra.toSMul.{u1, u3} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u3} π' (Semifield.toDivisionSemiring.{u3} π' (Field.toSemifield.{u3} π' (NormedField.toField.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u3} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u3} π' (NormedCommRing.toSeminormedCommRing.{u3} π' (NormedField.toNormedCommRing.{u3} π' (NontriviallyNormedField.toNormedField.{u3} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u4} π E (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u1, u4} π E (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u1, u4} π E (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)))))) (NegZeroClass.toZero.{u4} E (SubNegZeroMonoid.toNegZeroClass.{u4} E (SubtractionMonoid.toSubNegZeroMonoid.{u4} E (SubtractionCommMonoid.toSubtractionMonoid.{u4} E (AddCommGroup.toDivisionAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4))))))) (Module.toMulActionWithZero.{u1, u4} π E (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u4} E (SeminormedAddCommGroup.toAddCommGroup.{u4} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4))) (NormedSpace.toModule.{u1, u4} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u3, u4} π' E (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} E _inst_4) _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 (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 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)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} 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.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u3, u2} π' F (NontriviallyNormedField.toNormedField.{u3} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') x L)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_filter.restrict_scalars HasFDerivAtFilter.restrictScalarsβ'. -/
theorem HasFDerivAtFilter.restrictScalars {L} (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter f (f'.restrictScalars π) x L :=
h
#align has_fderiv_at_filter.restrict_scalars HasFDerivAtFilter.restrictScalars
+/- warning: has_fderiv_at.restrict_scalars -> HasFDerivAt.restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {x : E}, (HasFDerivAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x) -> (HasFDerivAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') x)
+but is expected to have type
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u4, u4, u3, u2} π' π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (RingHom.id.{u4} π' (Semiring.toNonAssocSemiring.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {x : E}, (HasFDerivAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x) -> (HasFDerivAt.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} π' E F (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (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_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u1, u4} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u4} π' (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _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 (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 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)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} 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.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at.restrict_scalars HasFDerivAt.restrictScalarsβ'. -/
theorem HasFDerivAt.restrictScalars (h : HasFDerivAt f f' x) :
HasFDerivAt f (f'.restrictScalars π) x :=
h
#align has_fderiv_at.restrict_scalars HasFDerivAt.restrictScalars
+/- warning: has_fderiv_within_at.restrict_scalars -> HasFDerivWithinAt.restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {s : Set.{u3} E} {x : E}, (HasFDerivWithinAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' s x) -> (HasFDerivWithinAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') s x)
+but is expected to have type
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u4, u4, u3, u2} π' π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (RingHom.id.{u4} π' (Semiring.toNonAssocSemiring.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {s : Set.{u3} E} {x : E}, (HasFDerivWithinAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' s x) -> (HasFDerivWithinAt.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} π' E F (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (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_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u1, u4} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u4} π' (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _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 (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 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)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} 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.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at.restrict_scalars HasFDerivWithinAt.restrictScalarsβ'. -/
theorem HasFDerivWithinAt.restrictScalars (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt f (f'.restrictScalars π) s x :=
h
#align has_fderiv_within_at.restrict_scalars HasFDerivWithinAt.restrictScalars
-theorem DifferentiableAt.restrict_scalars (h : DifferentiableAt π' f x) : DifferentiableAt π f x :=
+/- warning: differentiable_at.restrict_scalars -> DifferentiableAt.restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) -> (DifferentiableAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x)
+but is expected to have type
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) -> (DifferentiableAt.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x)
+Case conversion may be inaccurate. Consider using '#align differentiable_at.restrict_scalars DifferentiableAt.restrictScalarsβ'. -/
+theorem DifferentiableAt.restrictScalars (h : DifferentiableAt π' f x) : DifferentiableAt π f x :=
(h.HasFDerivAt.restrictScalars π).DifferentiableAt
-#align differentiable_at.restrict_scalars DifferentiableAt.restrict_scalars
-
-theorem DifferentiableWithinAt.restrict_scalars (h : DifferentiableWithinAt π' f s x) :
+#align differentiable_at.restrict_scalars DifferentiableAt.restrictScalars
+
+/- warning: differentiable_within_at.restrict_scalars -> DifferentiableWithinAt.restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E} {x : E}, (DifferentiableWithinAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s x) -> (DifferentiableWithinAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x)
+but is expected to have type
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E} {x : E}, (DifferentiableWithinAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s x) -> (DifferentiableWithinAt.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x)
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at.restrict_scalars DifferentiableWithinAt.restrictScalarsβ'. -/
+theorem DifferentiableWithinAt.restrictScalars (h : DifferentiableWithinAt π' f s x) :
DifferentiableWithinAt π f s x :=
(h.HasFDerivWithinAt.restrictScalars π).DifferentiableWithinAt
-#align differentiable_within_at.restrict_scalars DifferentiableWithinAt.restrict_scalars
-
-theorem DifferentiableOn.restrict_scalars (h : DifferentiableOn π' f s) : DifferentiableOn π f s :=
+#align differentiable_within_at.restrict_scalars DifferentiableWithinAt.restrictScalars
+
+/- warning: differentiable_on.restrict_scalars -> DifferentiableOn.restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E}, (DifferentiableOn.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s) -> (DifferentiableOn.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s)
+but is expected to have type
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E}, (DifferentiableOn.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s) -> (DifferentiableOn.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s)
+Case conversion may be inaccurate. Consider using '#align differentiable_on.restrict_scalars DifferentiableOn.restrictScalarsβ'. -/
+theorem DifferentiableOn.restrictScalars (h : DifferentiableOn π' f s) : DifferentiableOn π f s :=
fun x hx => (h x hx).restrictScalars π
-#align differentiable_on.restrict_scalars DifferentiableOn.restrict_scalars
-
-theorem Differentiable.restrict_scalars (h : Differentiable π' f) : Differentiable π f := fun x =>
+#align differentiable_on.restrict_scalars DifferentiableOn.restrictScalars
+
+/- warning: differentiable.restrict_scalars -> Differentiable.restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F}, (Differentiable.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f) -> (Differentiable.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f)
+but is expected to have type
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F}, (Differentiable.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f) -> (Differentiable.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f)
+Case conversion may be inaccurate. Consider using '#align differentiable.restrict_scalars Differentiable.restrictScalarsβ'. -/
+theorem Differentiable.restrictScalars (h : Differentiable π' f) : Differentiable π f := fun x =>
(h x).restrictScalars π
-#align differentiable.restrict_scalars Differentiable.restrict_scalars
-
+#align differentiable.restrict_scalars Differentiable.restrictScalars
+
+/- warning: has_fderiv_within_at_of_restrict_scalars -> hasFDerivWithinAt_of_restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {s : Set.{u3} E} {x : E} {g' : ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)}, (HasFDerivWithinAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f g' s x) -> (Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u2, 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(NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' 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(NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') g') -> (HasFDerivWithinAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' s x)
+but is expected to have type
+ forall (π : Type.{u4}) [_inst_1 : NontriviallyNormedField.{u4} π] {π' : Type.{u1}} [_inst_2 : NontriviallyNormedField.{u1} π'] [_inst_3 : NormedAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))] {E : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} E] [_inst_5 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_6 : NormedSpace.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u4, u1, u3} π π' E (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π' E (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π E (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u4, u1, u2} π π' F (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (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_8)))))) (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_2)))))) (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_8)))))) (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_2)))))) (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_8)))))) (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_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (Module.toMulActionWithZero.{u4, u2} π F (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : 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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {s : Set.{u3} E} {x : E} {g' : ContinuousLinearMap.{u4, u4, u3, u2} π π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)}, (HasFDerivWithinAt.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f g' s x) -> (Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u4, u4, u3, u2} π π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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 (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u1, u3, u2, u4} π' E F (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u4, u1} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u1} π' (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u4, u3} π E (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toSMul.{u4, u2} π F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u4, u2} π F (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') g') -> (HasFDerivWithinAt.{u1, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' s x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalarsβ'. -/
theorem hasFDerivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
(H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x :=
by
@@ -96,6 +150,12 @@ theorem hasFDerivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDeri
exact h
#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalars
+/- warning: has_fderiv_at_of_restrict_scalars -> hasFDerivAt_of_restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {f' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)} {x : E} {g' : ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)}, (HasFDerivAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f g' x) -> (Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) f') g') -> (HasFDerivAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x)
+but is expected to have type
+ forall (π : Type.{u4}) [_inst_1 : NontriviallyNormedField.{u4} π] {π' : Type.{u1}} [_inst_2 : NontriviallyNormedField.{u1} π'] [_inst_3 : NormedAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))] {E : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} E] [_inst_5 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_6 : NormedSpace.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u4, u1, u3} π π' E (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π' E (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π E (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u4, u1, u2} π π' F (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (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_8)))))) (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_2)))))) (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_8)))))) (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_2)))))) (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_8)))))) (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_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (Module.toMulActionWithZero.{u4, u2} π F (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {f' : 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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)} {x : E} {g' : ContinuousLinearMap.{u4, u4, u3, u2} π π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)}, (HasFDerivAt.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f g' x) -> (Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u4, u4, u3, u2} π π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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 (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u1, u3, u2, u4} π' E F (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u4, u1} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u1} π' (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u4, u3} π E (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toSMul.{u4, u2} π F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u4, u2} π F (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) f') g') -> (HasFDerivAt.{u1, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f f' x)
+Case conversion may be inaccurate. Consider using '#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalarsβ'. -/
theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f g' x)
(H : f'.restrictScalars π = g') : HasFDerivAt f f' x :=
by
@@ -103,11 +163,23 @@ theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f
exact h
#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalars
+/- warning: differentiable_at.fderiv_restrict_scalars -> DifferentiableAt.fderiv_restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) -> (Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)) (fderiv.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x) (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) (fderiv.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x)))
+but is expected to have type
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u4}} [_inst_2 : NontriviallyNormedField.{u4} π'] [_inst_3 : NormedAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _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)] [_inst_6 : NormedSpace.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u4, u3} π π' E (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π' E (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π' E (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π' E (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (DivisionSemiring.toSemiring.{u1} π (Semifield.toDivisionSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u4, u2} π π' F (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π' F (CommMonoidWithZero.toZero.{u4} π' (CommGroupWithZero.toCommMonoidWithZero.{u4} π' (Semifield.toCommGroupWithZero.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π' F (Semiring.toMonoidWithZero.{u4} π' (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))))) (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_8)))))) (Module.toMulActionWithZero.{u4, u2} π' F (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (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_8)))))) (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_8)))))) (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_8)))))) (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_8)) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) -> (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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (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_8) _inst_9)) (fderiv.{u1, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x) (ContinuousLinearMap.restrictScalars.{u4, u3, u2, u1} π' E F (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (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_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u1, u4} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u4} π' (NormedRing.toRing.{u4} π' (NormedCommRing.toNormedRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (Algebra.toSMul.{u1, u4} π π' (Semifield.toCommSemiring.{u1} π (Field.toSemifield.{u1} π (NormedField.toField.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (DivisionSemiring.toSemiring.{u4} π' (Semifield.toDivisionSemiring.{u4} π' (Field.toSemifield.{u4} π' (NormedField.toField.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u1, u4} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u4} π' (NormedCommRing.toSeminormedCommRing.{u4} π' (NormedField.toNormedCommRing.{u4} π' (NontriviallyNormedField.toNormedField.{u4} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π E (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u4, u3} π' E (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _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 (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u1, u2} π F (MonoidWithZero.toZero.{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))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} 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)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u1, u2} 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.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u1, u2} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u4, u2} π' F (NontriviallyNormedField.toNormedField.{u4} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) (fderiv.{u4, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x)))
+Case conversion may be inaccurate. Consider using '#align differentiable_at.fderiv_restrict_scalars DifferentiableAt.fderiv_restrictScalarsβ'. -/
theorem DifferentiableAt.fderiv_restrictScalars (h : DifferentiableAt π' f x) :
fderiv π f x = (fderiv π' f x).restrictScalars π :=
(h.HasFDerivAt.restrictScalars π).fderiv
#align differentiable_at.fderiv_restrict_scalars DifferentiableAt.fderiv_restrictScalars
+/- warning: differentiable_within_at_iff_restrict_scalars -> differentiableWithinAt_iff_restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E} {x : E}, (DifferentiableWithinAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x) -> (UniqueDiffWithinAt.{u1, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) s x) -> (Iff (DifferentiableWithinAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s x) (Exists.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)) (fun (g' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)) => Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) g') (fderivWithin.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x))))
+but is expected to have type
+ forall (π : Type.{u4}) [_inst_1 : NontriviallyNormedField.{u4} π] {π' : Type.{u1}} [_inst_2 : NontriviallyNormedField.{u1} π'] [_inst_3 : NormedAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))] {E : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} E] [_inst_5 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_6 : NormedSpace.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u4, u1, u3} π π' E (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π' E (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π E (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u4, u1, u2} π π' F (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (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_8)))))) (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_2)))))) (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_8)))))) (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_2)))))) (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_8)))))) (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_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (Module.toMulActionWithZero.{u4, u2} π F (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {s : Set.{u3} E} {x : E}, (DifferentiableWithinAt.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x) -> (UniqueDiffWithinAt.{u4, u3} π _inst_1 E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) s x) -> (Iff (DifferentiableWithinAt.{u1, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f s x) (Exists.{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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)) (fun (g' : 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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)) => Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u4, u4, u3, u2} π π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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 (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u1, u3, u2, u4} π' E F (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u4, u1} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u1} π' (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u4, u3} π E (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toSMul.{u4, u2} π F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u4, u2} π F (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) g') (fderivWithin.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f s x))))
+Case conversion may be inaccurate. Consider using '#align differentiable_within_at_iff_restrict_scalars differentiableWithinAt_iff_restrictScalarsβ'. -/
theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt π f s x)
(hs : UniqueDiffWithinAt π s x) :
DifferentiableWithinAt π' f s x β
@@ -120,6 +192,12 @@ theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt
exact β¨f', hasFDerivWithinAt_of_restrictScalars π hf.has_fderiv_within_at hf'β©
#align differentiable_within_at_iff_restrict_scalars differentiableWithinAt_iff_restrictScalars
+/- warning: differentiable_at_iff_restrict_scalars -> differentiableAt_iff_restrictScalars is a dubious translation:
+lean 3 declaration is
+ forall (π : Type.{u1}) [_inst_1 : NontriviallyNormedField.{u1} π] {π' : Type.{u2}} [_inst_2 : NontriviallyNormedField.{u2} π'] [_inst_3 : NormedAlgebra.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (SeminormedCommRing.toSemiNormedRing.{u2} π' (NormedCommRing.toSeminormedCommRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _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)] [_inst_6 : NormedSpace.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u1, u2, u3} π π' E (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u3} π' E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u2, u3} π' E (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u2, u3} π' E (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u2, u3} π' E (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u4}} [_inst_8 : NormedAddCommGroup.{u4} F] [_inst_9 : NormedSpace.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_10 : NormedSpace.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)] [_inst_11 : IsScalarTower.{u1, u2, u4} π π' F (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u2, u4} π' F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u2, u4} π' F (MulZeroClass.toHasZero.{u2} π' (MulZeroOneClass.toMulZeroClass.{u2} π' (MonoidWithZero.toMulZeroOneClass.{u2} π' (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u2, u4} π' F (Semiring.toMonoidWithZero.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u2, u4} π' F (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (SeminormedAddCommGroup.toAddCommGroup.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8))) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x) -> (Iff (DifferentiableAt.{u2, u3, u4} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) (Exists.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)) (fun (g' : ContinuousLinearMap.{u2, u2, u3, u4} π' π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (RingHom.id.{u2} π' (Semiring.toNonAssocSemiring.{u2} π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))) 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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10)) => Eq.{max (succ u3) (succ u4)} (ContinuousLinearMap.{u1, u1, u3, u4} 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.{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.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u2, u3, u4, u1} π' E F (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))) (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4) (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u4} F (PseudoMetricSpace.toUniformSpace.{u4} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u4} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8)))) π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1)))) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u4, u1, u2} E F (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) π π' (Ring.toSemiring.{u2} π' (NormedRing.toRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))) (SMulZeroClass.toHasSmul.{u1, u2} π π' (AddZeroClass.toHasZero.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} π π' (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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} π 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.{u2} π' (AddMonoid.toAddZeroClass.{u2} π' (AddCommMonoid.toAddMonoid.{u2} π' (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))))))))))) (Module.toMulActionWithZero.{u1, u2} π π' (Ring.toSemiring.{u1} π (NormedRing.toRing.{u1} π (NormedCommRing.toNormedRing.{u1} π (NormedField.toNormedCommRing.{u1} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} π' (SeminormedAddCommGroup.toAddCommGroup.{u2} π' (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))))) (NormedSpace.toModule.{u1, u2} π π' (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u2} π' (NonUnitalNormedRing.toNonUnitalSeminormedRing.{u2} π' (NormedRing.toNonUnitalNormedRing.{u2} π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2)))))) (NormedAlgebra.toNormedSpace'.{u1, u2} π (NontriviallyNormedField.toNormedField.{u1} π _inst_1) π' (NormedCommRing.toNormedRing.{u2} π' (NormedField.toNormedCommRing.{u2} π' (NontriviallyNormedField.toNormedField.{u2} π' _inst_2))) _inst_3)))))) (SMulZeroClass.toHasSmul.{u1, u3} π E (AddZeroClass.toHasZero.{u3} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (SMulWithZero.toSmulZeroClass.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π E (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} E (AddMonoid.toAddZeroClass.{u3} E (AddCommMonoid.toAddMonoid.{u3} E (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4))))) (Module.toMulActionWithZero.{u1, u3} π E (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} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π E (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u2, u3} π' E (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toHasSmul.{u1, u4} π F (AddZeroClass.toHasZero.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (SMulWithZero.toSmulZeroClass.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (MulActionWithZero.toSMulWithZero.{u1, u4} 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.{u4} F (AddMonoid.toAddZeroClass.{u4} F (AddCommMonoid.toAddMonoid.{u4} F (AddCommGroup.toAddCommMonoid.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8))))) (Module.toMulActionWithZero.{u1, u4} 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.{u4} F (NormedAddCommGroup.toAddCommGroup.{u4} F _inst_8)) (NormedSpace.toModule.{u1, u4} π F (NontriviallyNormedField.toNormedField.{u1} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u2, u4} π' F (NontriviallyNormedField.toNormedField.{u2} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u4} F _inst_8) _inst_10) _inst_11) g') (fderiv.{u1, u3, u4} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x))))
+but is expected to have type
+ forall (π : Type.{u4}) [_inst_1 : NontriviallyNormedField.{u4} π] {π' : Type.{u1}} [_inst_2 : NontriviallyNormedField.{u1} π'] [_inst_3 : NormedAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))] {E : Type.{u3}} [_inst_4 : NormedAddCommGroup.{u3} E] [_inst_5 : NormedSpace.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_6 : NormedSpace.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)] [_inst_7 : IsScalarTower.{u4, u1, u3} π π' E (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u1, u3} π' E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u1, u3} π' E (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_2)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u1, u3} π' E (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6))))) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)))))) (Module.toMulActionWithZero.{u4, u3} π E (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (NormedAddCommGroup.toAddCommGroup.{u3} E _inst_4)) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5)))))] {F : Type.{u2}} [_inst_8 : NormedAddCommGroup.{u2} F] [_inst_9 : NormedSpace.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_10 : NormedSpace.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)] [_inst_11 : IsScalarTower.{u4, u1, u2} π π' F (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (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_8)))))) (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_2)))))) (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_8)))))) (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_2)))))) (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_8)))))) (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_2))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10))))) (SMulZeroClass.toSMul.{u4, 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_8)))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (CommMonoidWithZero.toZero.{u4} π (CommGroupWithZero.toCommMonoidWithZero.{u4} π (Semifield.toCommGroupWithZero.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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_8)))))) (Module.toMulActionWithZero.{u4, u2} π F (DivisionSemiring.toSemiring.{u4} π (Semifield.toDivisionSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)))))] {f : E -> F} {x : E}, (DifferentiableAt.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x) -> (Iff (DifferentiableAt.{u1, u3, u2} π' _inst_2 E _inst_4 _inst_6 F _inst_8 _inst_10 f x) (Exists.{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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)) (fun (g' : 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_2))))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (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_2))))))) 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_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (NormedAddCommGroup.toAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10)) => Eq.{max (succ u3) (succ u2)} (ContinuousLinearMap.{u4, u4, u3, u2} π π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (RingHom.id.{u4} π (Semiring.toNonAssocSemiring.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} 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 (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) F (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9)) (ContinuousLinearMap.restrictScalars.{u1, u3, u2, u4} π' E F (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)) (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) (UniformSpace.toTopologicalSpace.{u3} E (PseudoMetricSpace.toUniformSpace.{u3} E (SeminormedAddCommGroup.toPseudoMetricSpace.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4)))) (UniformSpace.toTopologicalSpace.{u2} F (PseudoMetricSpace.toUniformSpace.{u2} F (SeminormedAddCommGroup.toPseudoMetricSpace.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8)))) π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9) (LinearMap.IsScalarTower.compatibleSMul.{u3, u2, u4, u1} E F (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) π π' (Ring.toSemiring.{u1} π' (NormedRing.toRing.{u1} π' (NormedCommRing.toNormedRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (Algebra.toSMul.{u4, u1} π π' (Semifield.toCommSemiring.{u4} π (Field.toSemifield.{u4} π (NormedField.toField.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))) (DivisionSemiring.toSemiring.{u1} π' (Semifield.toDivisionSemiring.{u1} π' (Field.toSemifield.{u1} π' (NormedField.toField.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2))))) (NormedAlgebra.toAlgebra.{u4, u1} π π' (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (SeminormedCommRing.toSeminormedRing.{u1} π' (NormedCommRing.toSeminormedCommRing.{u1} π' (NormedField.toNormedCommRing.{u1} π' (NontriviallyNormedField.toNormedField.{u1} π' _inst_2)))) _inst_3)) (SMulZeroClass.toSMul.{u4, u3} π E (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (SMulWithZero.toSMulZeroClass.{u4, u3} π E (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (MulActionWithZero.toSMulWithZero.{u4, u3} π E (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u3} E (SubNegZeroMonoid.toNegZeroClass.{u3} E (SubtractionMonoid.toSubNegZeroMonoid.{u3} E (SubtractionCommMonoid.toSubtractionMonoid.{u3} E (AddCommGroup.toDivisionAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))))))) (Module.toMulActionWithZero.{u4, u3} π E (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u3} E (SeminormedAddCommGroup.toAddCommGroup.{u3} E (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4))) (NormedSpace.toModule.{u4, u3} π E (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_5))))) (NormedSpace.toModule.{u1, u3} π' E (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u3} E _inst_4) _inst_6) _inst_7 (SMulZeroClass.toSMul.{u4, u2} π F (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (SMulWithZero.toSMulZeroClass.{u4, u2} π F (MonoidWithZero.toZero.{u4} π (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (MulActionWithZero.toSMulWithZero.{u4, u2} π F (Semiring.toMonoidWithZero.{u4} π (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1)))))) (NegZeroClass.toZero.{u2} F (SubNegZeroMonoid.toNegZeroClass.{u2} F (SubtractionMonoid.toSubNegZeroMonoid.{u2} F (SubtractionCommMonoid.toSubtractionMonoid.{u2} F (AddCommGroup.toDivisionAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))))))) (Module.toMulActionWithZero.{u4, u2} π F (Ring.toSemiring.{u4} π (NormedRing.toRing.{u4} π (NormedCommRing.toNormedRing.{u4} π (NormedField.toNormedCommRing.{u4} π (NontriviallyNormedField.toNormedField.{u4} π _inst_1))))) (AddCommGroup.toAddCommMonoid.{u2} F (SeminormedAddCommGroup.toAddCommGroup.{u2} F (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8))) (NormedSpace.toModule.{u4, u2} π F (NontriviallyNormedField.toNormedField.{u4} π _inst_1) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_9))))) (NormedSpace.toModule.{u1, u2} π' F (NontriviallyNormedField.toNormedField.{u1} π' _inst_2) (NormedAddCommGroup.toSeminormedAddCommGroup.{u2} F _inst_8) _inst_10) _inst_11) g') (fderiv.{u4, u3, u2} π _inst_1 E _inst_4 _inst_5 F _inst_8 _inst_9 f x))))
+Case conversion may be inaccurate. Consider using '#align differentiable_at_iff_restrict_scalars differentiableAt_iff_restrictScalarsβ'. -/
theorem differentiableAt_iff_restrictScalars (hf : DifferentiableAt π f x) :
DifferentiableAt π' f x β β g' : E βL[π'] F, g'.restrictScalars π = fderiv π f x :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952
@@ -52,33 +52,33 @@ variable [IsScalarTower π π' F]
variable {f : E β F} {f' : E βL[π'] F} {s : Set E} {x : E}
-theorem HasStrictFderivAt.restrictScalars (h : HasStrictFderivAt f f' x) :
- HasStrictFderivAt f (f'.restrictScalars π) x :=
+theorem HasStrictFDerivAt.restrictScalars (h : HasStrictFDerivAt f f' x) :
+ HasStrictFDerivAt f (f'.restrictScalars π) x :=
h
-#align has_strict_fderiv_at.restrict_scalars HasStrictFderivAt.restrictScalars
+#align has_strict_fderiv_at.restrict_scalars HasStrictFDerivAt.restrictScalars
-theorem HasFderivAtFilter.restrictScalars {L} (h : HasFderivAtFilter f f' x L) :
- HasFderivAtFilter f (f'.restrictScalars π) x L :=
+theorem HasFDerivAtFilter.restrictScalars {L} (h : HasFDerivAtFilter f f' x L) :
+ HasFDerivAtFilter f (f'.restrictScalars π) x L :=
h
-#align has_fderiv_at_filter.restrict_scalars HasFderivAtFilter.restrictScalars
+#align has_fderiv_at_filter.restrict_scalars HasFDerivAtFilter.restrictScalars
-theorem HasFderivAt.restrictScalars (h : HasFderivAt f f' x) :
- HasFderivAt f (f'.restrictScalars π) x :=
+theorem HasFDerivAt.restrictScalars (h : HasFDerivAt f f' x) :
+ HasFDerivAt f (f'.restrictScalars π) x :=
h
-#align has_fderiv_at.restrict_scalars HasFderivAt.restrictScalars
+#align has_fderiv_at.restrict_scalars HasFDerivAt.restrictScalars
-theorem HasFderivWithinAt.restrictScalars (h : HasFderivWithinAt f f' s x) :
- HasFderivWithinAt f (f'.restrictScalars π) s x :=
+theorem HasFDerivWithinAt.restrictScalars (h : HasFDerivWithinAt f f' s x) :
+ HasFDerivWithinAt f (f'.restrictScalars π) s x :=
h
-#align has_fderiv_within_at.restrict_scalars HasFderivWithinAt.restrictScalars
+#align has_fderiv_within_at.restrict_scalars HasFDerivWithinAt.restrictScalars
theorem DifferentiableAt.restrict_scalars (h : DifferentiableAt π' f x) : DifferentiableAt π f x :=
- (h.HasFderivAt.restrictScalars π).DifferentiableAt
+ (h.HasFDerivAt.restrictScalars π).DifferentiableAt
#align differentiable_at.restrict_scalars DifferentiableAt.restrict_scalars
theorem DifferentiableWithinAt.restrict_scalars (h : DifferentiableWithinAt π' f s x) :
DifferentiableWithinAt π f s x :=
- (h.HasFderivWithinAt.restrictScalars π).DifferentiableWithinAt
+ (h.HasFDerivWithinAt.restrictScalars π).DifferentiableWithinAt
#align differentiable_within_at.restrict_scalars DifferentiableWithinAt.restrict_scalars
theorem DifferentiableOn.restrict_scalars (h : DifferentiableOn π' f s) : DifferentiableOn π f s :=
@@ -89,23 +89,23 @@ theorem Differentiable.restrict_scalars (h : Differentiable π' f) : Different
(h x).restrictScalars π
#align differentiable.restrict_scalars Differentiable.restrict_scalars
-theorem hasFderivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFderivWithinAt f g' s x)
- (H : f'.restrictScalars π = g') : HasFderivWithinAt f f' s x :=
+theorem hasFDerivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
+ (H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x :=
by
rw [β H] at h
exact h
-#align has_fderiv_within_at_of_restrict_scalars hasFderivWithinAt_of_restrictScalars
+#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalars
-theorem hasFderivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFderivAt f g' x)
- (H : f'.restrictScalars π = g') : HasFderivAt f f' x :=
+theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f g' x)
+ (H : f'.restrictScalars π = g') : HasFDerivAt f f' x :=
by
rw [β H] at h
exact h
-#align has_fderiv_at_of_restrict_scalars hasFderivAt_of_restrictScalars
+#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalars
theorem DifferentiableAt.fderiv_restrictScalars (h : DifferentiableAt π' f x) :
fderiv π f x = (fderiv π' f x).restrictScalars π :=
- (h.HasFderivAt.restrictScalars π).fderiv
+ (h.HasFDerivAt.restrictScalars π).fderiv
#align differentiable_at.fderiv_restrict_scalars DifferentiableAt.fderiv_restrictScalars
theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt π f s x)
@@ -117,7 +117,7 @@ theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt
Β· rintro β¨g', hg'β©
exact β¨g', hs.eq (hg'.restrict_scalars π) hf.has_fderiv_within_atβ©
Β· rintro β¨f', hf'β©
- exact β¨f', hasFderivWithinAt_of_restrictScalars π hf.has_fderiv_within_at hf'β©
+ exact β¨f', hasFDerivWithinAt_of_restrictScalars π hf.has_fderiv_within_at hf'β©
#align differentiable_within_at_iff_restrict_scalars differentiableWithinAt_iff_restrictScalars
theorem differentiableAt_iff_restrictScalars (hf : DifferentiableAt π f x) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -37,17 +37,11 @@ respectively by `π'` and `π` where `π'` is a normed algebra over `π`
variable (π : Type*) [NontriviallyNormedField π]
-
variable {π' : Type*} [NontriviallyNormedField π'] [NormedAlgebra π π']
-
variable {E : Type*} [NormedAddCommGroup E] [NormedSpace π E] [NormedSpace π' E]
-
variable [IsScalarTower π π' E]
-
variable {F : Type*} [NormedAddCommGroup F] [NormedSpace π F] [NormedSpace π' F]
-
variable [IsScalarTower π π' F]
-
variable {f : E β F} {f' : E βL[π'] F} {s : Set E} {x : E}
@[fun_prop]
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.
@@ -50,6 +50,7 @@ variable [IsScalarTower π π' F]
variable {f : E β F} {f' : E βL[π'] F} {s : Set E} {x : E}
+@[fun_prop]
theorem HasStrictFDerivAt.restrictScalars (h : HasStrictFDerivAt f f' x) :
HasStrictFDerivAt f (f'.restrictScalars π) x :=
h
@@ -60,39 +61,47 @@ theorem HasFDerivAtFilter.restrictScalars {L} (h : HasFDerivAtFilter f f' x L) :
.of_isLittleO h.1
#align has_fderiv_at_filter.restrict_scalars HasFDerivAtFilter.restrictScalars
+@[fun_prop]
theorem HasFDerivAt.restrictScalars (h : HasFDerivAt f f' x) :
HasFDerivAt f (f'.restrictScalars π) x :=
.of_isLittleO h.1
#align has_fderiv_at.restrict_scalars HasFDerivAt.restrictScalars
+@[fun_prop]
theorem HasFDerivWithinAt.restrictScalars (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt f (f'.restrictScalars π) s x :=
.of_isLittleO h.1
#align has_fderiv_within_at.restrict_scalars HasFDerivWithinAt.restrictScalars
+@[fun_prop]
theorem DifferentiableAt.restrictScalars (h : DifferentiableAt π' f x) : DifferentiableAt π f x :=
(h.hasFDerivAt.restrictScalars π).differentiableAt
#align differentiable_at.restrict_scalars DifferentiableAt.restrictScalars
+@[fun_prop]
theorem DifferentiableWithinAt.restrictScalars (h : DifferentiableWithinAt π' f s x) :
DifferentiableWithinAt π f s x :=
(h.hasFDerivWithinAt.restrictScalars π).differentiableWithinAt
#align differentiable_within_at.restrict_scalars DifferentiableWithinAt.restrictScalars
+@[fun_prop]
theorem DifferentiableOn.restrictScalars (h : DifferentiableOn π' f s) : DifferentiableOn π f s :=
fun x hx => (h x hx).restrictScalars π
#align differentiable_on.restrict_scalars DifferentiableOn.restrictScalars
+@[fun_prop]
theorem Differentiable.restrictScalars (h : Differentiable π' f) : Differentiable π f := fun x =>
(h x).restrictScalars π
#align differentiable.restrict_scalars Differentiable.restrictScalars
+@[fun_prop]
theorem HasFDerivWithinAt.of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
(H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x := by
rw [β H] at h
exact .of_isLittleO h.1
#align has_fderiv_within_at_of_restrict_scalars HasFDerivWithinAt.of_restrictScalars
+@[fun_prop]
theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f g' x)
(H : f'.restrictScalars π = g') : HasFDerivAt f f' x := by
rw [β H] at h
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.
@@ -20,7 +20,8 @@ the scalar restriction of a linear map.
open Filter Asymptotics ContinuousLinearMap Set Metric
-open Topology Classical NNReal Filter Asymptotics ENNReal
+open scoped Classical
+open Topology NNReal Filter Asymptotics ENNReal
noncomputable section
structure
(#8907)
This way we can easily change the definition so that it works for topological vector spaces without generalizing any of the theorems right away.
@@ -56,17 +56,17 @@ theorem HasStrictFDerivAt.restrictScalars (h : HasStrictFDerivAt f f' x) :
theorem HasFDerivAtFilter.restrictScalars {L} (h : HasFDerivAtFilter f f' x L) :
HasFDerivAtFilter f (f'.restrictScalars π) x L :=
- h
+ .of_isLittleO h.1
#align has_fderiv_at_filter.restrict_scalars HasFDerivAtFilter.restrictScalars
theorem HasFDerivAt.restrictScalars (h : HasFDerivAt f f' x) :
HasFDerivAt f (f'.restrictScalars π) x :=
- h
+ .of_isLittleO h.1
#align has_fderiv_at.restrict_scalars HasFDerivAt.restrictScalars
theorem HasFDerivWithinAt.restrictScalars (h : HasFDerivWithinAt f f' s x) :
HasFDerivWithinAt f (f'.restrictScalars π) s x :=
- h
+ .of_isLittleO h.1
#align has_fderiv_within_at.restrict_scalars HasFDerivWithinAt.restrictScalars
theorem DifferentiableAt.restrictScalars (h : DifferentiableAt π' f x) : DifferentiableAt π f x :=
@@ -86,16 +86,16 @@ theorem Differentiable.restrictScalars (h : Differentiable π' f) : Differenti
(h x).restrictScalars π
#align differentiable.restrict_scalars Differentiable.restrictScalars
-theorem hasFDerivWithinAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
+theorem HasFDerivWithinAt.of_restrictScalars {g' : E βL[π] F} (h : HasFDerivWithinAt f g' s x)
(H : f'.restrictScalars π = g') : HasFDerivWithinAt f f' s x := by
rw [β H] at h
- exact h
-#align has_fderiv_within_at_of_restrict_scalars hasFDerivWithinAt_of_restrictScalars
+ exact .of_isLittleO h.1
+#align has_fderiv_within_at_of_restrict_scalars HasFDerivWithinAt.of_restrictScalars
theorem hasFDerivAt_of_restrictScalars {g' : E βL[π] F} (h : HasFDerivAt f g' x)
(H : f'.restrictScalars π = g') : HasFDerivAt f f' x := by
rw [β H] at h
- exact h
+ exact .of_isLittleO h.1
#align has_fderiv_at_of_restrict_scalars hasFDerivAt_of_restrictScalars
theorem DifferentiableAt.fderiv_restrictScalars (h : DifferentiableAt π' f x) :
@@ -110,7 +110,7 @@ theorem differentiableWithinAt_iff_restrictScalars (hf : DifferentiableWithinAt
Β· rintro β¨g', hg'β©
exact β¨g', hs.eq (hg'.restrictScalars π) hf.hasFDerivWithinAtβ©
Β· rintro β¨f', hf'β©
- exact β¨f', hasFDerivWithinAt_of_restrictScalars π hf.hasFDerivWithinAt hf'β©
+ exact β¨f', hf.hasFDerivWithinAt.of_restrictScalars π hf'β©
#align differentiable_within_at_iff_restrict_scalars differentiableWithinAt_iff_restrictScalars
theorem differentiableAt_iff_restrictScalars (hf : DifferentiableAt π f x) :
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -35,15 +35,15 @@ respectively by `π'` and `π` where `π'` is a normed algebra over `π`
-/
-variable (π : Type _) [NontriviallyNormedField π]
+variable (π : Type*) [NontriviallyNormedField π]
-variable {π' : Type _} [NontriviallyNormedField π'] [NormedAlgebra π π']
+variable {π' : Type*} [NontriviallyNormedField π'] [NormedAlgebra π π']
-variable {E : Type _} [NormedAddCommGroup E] [NormedSpace π E] [NormedSpace π' E]
+variable {E : Type*} [NormedAddCommGroup E] [NormedSpace π E] [NormedSpace π' E]
variable [IsScalarTower π π' E]
-variable {F : Type _} [NormedAddCommGroup F] [NormedSpace π F] [NormedSpace π' F]
+variable {F : Type*} [NormedAddCommGroup F] [NormedSpace π F] [NormedSpace π' F]
variable [IsScalarTower π π' F]
@@ -2,14 +2,11 @@
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, SΓ©bastien GouΓ«zel, Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.calculus.fderiv.restrict_scalars
-! leanprover-community/mathlib commit e3fb84046afd187b710170887195d50bada934ee
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Analysis.Calculus.FDeriv.Basic
+#align_import analysis.calculus.fderiv.restrict_scalars from "leanprover-community/mathlib"@"e3fb84046afd187b710170887195d50bada934ee"
+
/-!
# The derivative of the scalar restriction of a linear map
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